To determine the area bounded by the curve y = 2ˣ, the x-axis, and the ordinates x = 0 and x = 4, we are required to compute the definite integral of 2ˣ from x = 0 to x = 4. Step 1: Write down the integral The area is given by: A = ∫₀⁴ 2ˣ dx Step 2: Evaluate the integral The integral of 2ˣ is: ∫ 2ˣRead more
To determine the area bounded by the curve y = 2ˣ, the x-axis, and the ordinates x = 0 and x = 4, we are required to compute the definite integral of 2ˣ from x = 0 to x = 4.
Step 1: Write down the integral
The area is given by:
A = ∫₀⁴ 2ˣ dx
Step 2: Evaluate the integral
The integral of 2ˣ is:
∫ 2ˣ dx = (2ˣ) / ln 2
Now, calculate the area under the curve from x = 0 to x = 4:
To determine the antiderivative (indefinite integral) of I = ∫ (tan x - 1) / (tan x + 1) dx Step 1: Substituting x in terms of a trigonometric identity We apply the identity : tan(A - B) = (tan A - tan B) / (1 + tan A tan B) Here, we choose A = π/4 and B = x, so tan(π/4 - x) = (tan(π/4) - tan x) / (Read more
To determine the antiderivative (indefinite integral) of
I = ∫ (tan x – 1) / (tan x + 1) dx
Step 1: Substituting x in terms of a trigonometric identity
We apply the identity :
tan(A – B) = (tan A – tan B) / (1 + tan A tan B)
Here, we choose A = π/4 and B = x, so
tan(π/4 – x) = (tan(π/4) – tan x) / (1 + tan(π/4) tan x)
Since tan(π/4) = 1, this reduces to:
tan(π/4 – x) = (1 – tan x) / (1 + tan x)
Taking the negative,
– tan(π/4 – x) = (tan x – 1) / (tan x + 1)
So, our integral is:
I = ∫ – tan(π/4 – x) dx
Step 2: Finding the Integral
We know:
∫ tan u du = log | sec u | + C
Substituting u = π/4 – x, we get:
I = – ∫ tan(π/4 – x) dx
= – log | sec(π/4 – x) | + C
Conclusion
Therefore, the right answer is: – log | sec(π/4 – x) | + C
The rate of energy emitted by a black body is governed by the Stefan-Boltzmann law, which states that the energy radiated per unit area is proportional to the fourth power of the temperature: E ∝ T⁴ So, for a black body at a temperature of 300 K, the energy emitted will be proportional to: 300⁴ ThusRead more
The rate of energy emitted by a black body is governed by the Stefan-Boltzmann law, which states that the energy radiated per unit area is proportional to the fourth power of the temperature:
E ∝ T⁴
So, for a black body at a temperature of 300 K, the energy emitted will be proportional to:
The Stefan-Boltzmann law states that the brightness of an object depends on its temperature and emissivity. Black objects have the highest emissivity, meaning they can emit and absorb radiation more efficiently than grey or white objects. Since all objects can withstand the same maximum temperatureRead more
The Stefan-Boltzmann law states that the brightness of an object depends on its temperature and emissivity. Black objects have the highest emissivity, meaning they can emit and absorb radiation more efficiently than grey or white objects.
Since all objects can withstand the same maximum temperature of 2,800°C, the black object will glow the brightest because it has the highest emissivity and thus radiates energy more efficiently.
Transmittance describes the amount of heat radiation received by a material divided by that amount received. Transmittance is how much radiation can transmit through the surface of the body compared to its incidence on a body. In this context, the right term is: Transmittance
Transmittance describes the amount of heat radiation received by a material divided by that amount received.
Transmittance is how much radiation can transmit through the surface of the body compared to its incidence on a body.
The area bounded by the curve y = 2ˣ, x – axis, ordinates x = 0 and x = 4 is
To determine the area bounded by the curve y = 2ˣ, the x-axis, and the ordinates x = 0 and x = 4, we are required to compute the definite integral of 2ˣ from x = 0 to x = 4. Step 1: Write down the integral The area is given by: A = ∫₀⁴ 2ˣ dx Step 2: Evaluate the integral The integral of 2ˣ is: ∫ 2ˣRead more
To determine the area bounded by the curve y = 2ˣ, the x-axis, and the ordinates x = 0 and x = 4, we are required to compute the definite integral of 2ˣ from x = 0 to x = 4.
Step 1: Write down the integral
The area is given by:
A = ∫₀⁴ 2ˣ dx
Step 2: Evaluate the integral
The integral of 2ˣ is:
∫ 2ˣ dx = (2ˣ) / ln 2
Now, calculate the area under the curve from x = 0 to x = 4:
A = [(2ˣ) / ln 2]₀⁴
At x = 4:
(2⁴) / ln 2 = 16 / ln 2
At x = 0:
(2⁰) / ln 2 = 1 / ln 2
Therefore, the area:
A = (16 / ln 2) – (1 / ln 2) = 15 / ln 2
Step 3: Final result
So the region is:
A = 15 / ln 2 square units
Click here:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-12/maths/#chapter-8
Anti-derivative of (tan x – 1)/(tan x + 1) with respect to x is
To determine the antiderivative (indefinite integral) of I = ∫ (tan x - 1) / (tan x + 1) dx Step 1: Substituting x in terms of a trigonometric identity We apply the identity : tan(A - B) = (tan A - tan B) / (1 + tan A tan B) Here, we choose A = π/4 and B = x, so tan(π/4 - x) = (tan(π/4) - tan x) / (Read more
To determine the antiderivative (indefinite integral) of
I = ∫ (tan x – 1) / (tan x + 1) dx
Step 1: Substituting x in terms of a trigonometric identity
We apply the identity :
tan(A – B) = (tan A – tan B) / (1 + tan A tan B)
Here, we choose A = π/4 and B = x, so
tan(π/4 – x) = (tan(π/4) – tan x) / (1 + tan(π/4) tan x)
Since tan(π/4) = 1, this reduces to:
tan(π/4 – x) = (1 – tan x) / (1 + tan x)
Taking the negative,
– tan(π/4 – x) = (tan x – 1) / (tan x + 1)
So, our integral is:
I = ∫ – tan(π/4 – x) dx
Step 2: Finding the Integral
We know:
∫ tan u du = log | sec u | + C
Substituting u = π/4 – x, we get:
I = – ∫ tan(π/4 – x) dx
= – log | sec(π/4 – x) | + C
Conclusion
Therefore, the right answer is: – log | sec(π/4 – x) | + C
Click here for more:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-12/maths/#chapter-8
A black body is at a temperature 300 K. It emits energy at a rate, which is proportional to
The rate of energy emitted by a black body is governed by the Stefan-Boltzmann law, which states that the energy radiated per unit area is proportional to the fourth power of the temperature: E ∝ T⁴ So, for a black body at a temperature of 300 K, the energy emitted will be proportional to: 300⁴ ThusRead more
The rate of energy emitted by a black body is governed by the Stefan-Boltzmann law, which states that the energy radiated per unit area is proportional to the fourth power of the temperature:
E ∝ T⁴
So, for a black body at a temperature of 300 K, the energy emitted will be proportional to:
300⁴
Thus, the correct answer is: 300⁴
Click here:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-10/
Three objects coloured black, grey and white can withstand hostile conditions upto 2,800° C. Which object will glow brightest?
The Stefan-Boltzmann law states that the brightness of an object depends on its temperature and emissivity. Black objects have the highest emissivity, meaning they can emit and absorb radiation more efficiently than grey or white objects. Since all objects can withstand the same maximum temperatureRead more
The Stefan-Boltzmann law states that the brightness of an object depends on its temperature and emissivity. Black objects have the highest emissivity, meaning they can emit and absorb radiation more efficiently than grey or white objects.
Since all objects can withstand the same maximum temperature of 2,800°C, the black object will glow the brightest because it has the highest emissivity and thus radiates energy more efficiently.
So, the correct answer is: the black object
Click here:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-10/
Ratio of the amount of heat radiation, transmitted through the body to the amount of heat radiation incident on it, is known as
Transmittance describes the amount of heat radiation received by a material divided by that amount received. Transmittance is how much radiation can transmit through the surface of the body compared to its incidence on a body. In this context, the right term is: Transmittance
Transmittance describes the amount of heat radiation received by a material divided by that amount received.
Transmittance is how much radiation can transmit through the surface of the body compared to its incidence on a body.
In this context, the right term is: Transmittance
See less