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Free CBSE - Class 12 Mathematics - Application of Integrals worksheets

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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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