CBSE - Class 12 Mathematics Application of Integrals Worksheet
1.
Find the area bounded by the curve $y = \sin x$ between $x = 0$ and $x = 2\pi$.
2.
Sketch the graph of $y = |x + 3|$ and evaluate $\int_{-6}^{0} |x + 3| dx$.
3.
Find the area under the given curves and given lines: (ii) $y = x^4$, $x = 1$, $x = 5$ and $x$-axis
4.
Find the area under the given curves and given lines: (i) $y = x^2$, $x = 1$, $x = 2$ and $x$-axis
5.
Area bounded by the curve $y = x^3$, the $x$-axis and the ordinates $x = – 2$ and $x = 1$ is
a.
– 9
b.
$\frac{-15}{4}$
c.
$\frac{15}{4}$
d.
$\frac{17}{4}$
6.
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 $x < 0$].
a.
0
b.
$\frac{1}{3}$
c.
$\frac{2}{3}$
d.
$\frac{4}{3}$
7.
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
a.
$\pi$
b.
$\frac{\pi}{2}$
c.
$\frac{\pi}{3}$
d.
$\frac{\pi}{4}$
8.
Find the area of the region bounded by the ellipse $\frac{x^2}{16} + \frac{y^2}{9} = 1$.
9.
Find the area of the region bounded by the ellipse $\frac{x^2}{4} + \frac{y^2}{9} = 1$.
10.
Area of the region bounded by the curve $y^2 = 4x$, $y$-axis and the line $y = 3$ is
a.
2
b.
$\frac{9}{4}$
c.
$\frac{9}{3}$
d.
$\frac{9}{2}$
