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CBSE - Class 12 > Mathematics > Application of Integrals Worksheets

Free CBSE - Class 12 Mathematics - Application of Integrals worksheets

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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

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

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