The area of the region bounded by the curve y = x + 1 and the lines x = 2, x = 3 and x-axis in sq. units is
The x-axis is the horizontal axis in a Cartesian coordinate system. It represents the independent variable and is typically used to plot values of x. Points on the x-axis have a y-coordinate of zero. It helps in graphing functions and analyzing relationships between variables in mathematics.
Class 12 Maths Chapter 8 Applications of Integrals is an important topic for the CBSE Exam 2024-25. It covers the calculation of areas between curves and the determination of volumes of solids using integration. The chapter has practical applications in physics and engineering. Mastering these concepts is essential for solving real-life problems and higher studies.
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In order to find the area of the region determined by the curve y = x + 1 along with the lines x = 2, x = 3 and the x-axis, we first need to set up the definite integral.
Step 1: Set up the integral
To calculate the area, we will integrate the function y = x + 1 with respect to x between the limits x = 2 and x = 3.
A = ∫₂³ (x + 1) dx
Step 2: Integrate the function
First, integrate (x + 1):
∫ (x + 1) dx = (x²)/2 + x
Now, evaluate this from x = 2 to x = 3:
At x = 3:
(3²)/2 + 3 = 9/2 + 3 = 9/2 + 6/2 = 15/2
At x = 2:
(2²)/2 + 2 = 4/2 + 2 = 2 + 2 = 4
Step 3: Find the area
A= 15/2 – 4 = 15/2 – 8/2 = 7/2
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