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CBSE - Class 12 > Mathematics > Application of Integrals Worksheets

Free CBSE - Class 12 Mathematics - Application of Integrals worksheets

Sample Worksheets

Here is a Sample Worksheet for you to Practice. Download this worksheet to see the answers.

1.
Area bounded by the curve $y = x^3$, the $x$-axis and the ordinates $x = – 2$ and $x = 1$ is
1. – 9 2. $\frac{-15}{4}$ 3. $\frac{15}{4}$ 4. $\frac{17}{4}$
2.
The area bounded by the curve $y = x | x |$, $x$-axis and the ordinates $x = – 1$ and $x = 1$ is given by
[Hint : $y = x^2$ if $x > 0$ and $y = – x^2$ if $x < 0$].
1. 0 2. $\frac{1}{3}$ 3. $\frac{2}{3}$ 4. $\frac{4}{3}$
3.
Find the area of the region bounded by the ellipse $\frac{x^2}{16} + \frac{y^2}{9} = 1$.
4.
Find the area of the region bounded by the ellipse $\frac{x^2}{4} + \frac{y^2}{9} = 1$.
5.
Area lying in the first quadrant and bounded by the circle $x^2 + y^2 = 4$ and the lines $x = 0$ and $x = 2$ is
1. $\pi$ 2. $\frac{\pi}{2}$ 3. $\frac{\pi}{3}$ 4. $\frac{\pi}{4}$
6.
Area of the region bounded by the curve $y^2 = 4x$, $y$-axis and the line $y = 3$ is
1. 2 2. $\frac{9}{4}$ 3. $\frac{9}{3}$ 4. $\frac{9}{2}$
7.
Find the area under the given curves and given lines:
(i) $y = x^2$, $x = 1$, $x = 2$ and $x$-axis
8.
Find the area under the given curves and given lines:
(ii) $y = x^4$, $x = 1$, $x = 5$ and $x$-axis
9.
Sketch the graph of $y = |x + 3|$ and evaluate $\int_{-6}^{0} |x + 3| dx$.
10.
Find the area bounded by the curve $y = \sin x$ between $x = 0$ and $x = 2\pi$.
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Chapters in CBSE - Class 12 Mathematics

Application of Derivatives Worksheet Continuity and Differentiability Worksheet Determinants Worksheet Differential Equations Worksheet Integrals Worksheet Inverse Trigonometric Functions Worksheet Linear Programming Worksheet Matrices Worksheet Probability Worksheet Relations and Functions Worksheet Three Dimensional Geometry Worksheet Vector Algebra Worksheet

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