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  1. (c) Solid CO2 is called dry ice because it does not wet on evaporation and directly changes into vapours. https://www.tiwariacademy.com/ncert-solutions/class-9/science/chapter-1/

    (c) Solid CO2 is called dry ice because it does not wet on evaporation and directly changes into vapours.

    https://www.tiwariacademy.com/ncert-solutions/class-9/science/chapter-1/

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  2. Determine the area of the region bounded by the curve xy = 4 and the lines x = 1, x = 3, and the x-axis. First we rewrite the equation xy = 4 to solve for y in terms of x. Now solving the above equation for y we get, y = 4/x Step 1 We begin by setting up the integral The area can be calculated by inRead more

    Determine the area of the region bounded by the curve xy = 4 and the lines x = 1, x = 3, and the x-axis. First we rewrite the equation xy = 4 to solve for y in terms of x.

    Now solving the above equation for y we get,
    y = 4/x

    Step 1
    We begin by setting up the integral
    The area can be calculated by integrating y = 4/x from x = 1 to x = 3:

    A = ∫₁³ (4/x) dx

    Step 2: Evaluate the integral
    We know that:

    ∫ (1/x) dx = ln |x|

    Thus, the integral becomes:

    A = 4 ∫₁³ (1/x) dx = 4 [ln x]₁³

    Step 3: Calculate the area
    At x = 3:

    ln 3

    At x = 1:

    ln 1 = 0

    Therefore, the area is

    A = 4 (ln 3 – 0) = 4 ln 3

    Using logarithmic properties:

    A = ln (3⁴) = ln 81

    Click here for more:
    https://www.tiwariacademy.com/ncert-solutions/class-12/maths/#chapter-8

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  3. To find the area bounded by the curve y = sin x, the x-axis, and the ordinates x = 0 and x = 2, we must calculate the definite integral of sin x from 0 to 2. Step 1: Set up the integral The area is given by: A = ∫₀² sin x dx Step 2: Solve the integral We know the integral of sin x is: ∫ sin x dx = -Read more

    To find the area bounded by the curve y = sin x, the x-axis, and the ordinates x = 0 and x = 2, we must calculate the definite integral of sin x from 0 to 2.
    Step 1: Set up the integral
    The area is given by:

    A = ∫₀² sin x dx

    Step 2: Solve the integral
    We know the integral of sin x is:

    ∫ sin x dx = -cos x

    Now, evaluate the integral from 0 to 2:

    A = [-cos x]₀²

    At x = 2:

    -cos(2)

    At x = 0:

    -cos(0) = -1

    Thus, the area is:

    A = -cos(2) – (-1) = 1 + cos(2)

    Step 3: Approximate the result
    Using a calculator, cos(2) ≈ -0.416, so:

    A ≈ 1 – (-0.416) = 1 + 0.416 = 1.416

    Thus, the closest option to this result is: 4/3 sq. units.

    Click here for more:
    https://www.tiwariacademy.com/ncert-solutions/class-12/maths/#chapter-8

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