Application of Integrals - Gujarat Board (GSEB) STD 12 Science Maths Questions

Q 1M.C.Q (1 Marks)1 Mark

The area of the region bounded by the circle $x^2+y^2$ $=9$ in the first quadrant is :

A
$9 \pi$
B
$\frac{3 \pi}{4}$
✓
$\frac{9 \pi}{4}$
D
$3 \pi$

Answer: C.

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Q 2M.C.Q (1 Marks)1 Mark

Area bounded by curve $y^2=4 x, y$-axis and line $y=3$ is:

A
2
✓
$\frac{9}{4}$
C
$\frac{9}{3}$
D
$\frac{9}{2}$.

Answer: B.

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Q 3M.C.Q (1 Marks)1 Mark

Area of circle $x^2+y^2=4$ :

A
$2 \pi$
B
$16 \pi$
✓
$4 \pi$
D
$\frac{\pi}{4}$

Answer: C.

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Q 4M.C.Q (1 Marks)1 Mark

The area of the region bounded by the curve $y=x^2$ and line $y=4$ is:

A
$\frac{33}{2}$
B
$\frac{8}{3}$
C
$\frac{32}{3}$
D
$\frac{4}{3}$

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Q 5M.C.Q (1 Marks)1 Mark

The area of the region bounded by the parabola $y=\sin ^2 x$, lines $x=\frac{\pi}{2}, x=\pi$ and $x$-axis is :

A
$\frac{\pi}{2}$
B
$\frac{\pi}{4}$
C
$\frac{\pi}{8}$
D
$\pi$.

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Q 61 Marks Question1 Mark

Find the area of the region bounded by the curve $y=\cos x$ and the $x$-axis when $0 \leq x \leq \pi$.

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Q 71 Marks Question1 Mark

Find the area of the region bounded by the curve $y=x^2$ and the lines $x=0$ and $x=2$.

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Q 81 Marks Question1 Mark

Find the area bounded by the curve $y=\sin x$, the ordinate $x=\frac{\pi}{2}$ and the $x$-axis.

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Q 91 Marks Question1 Mark

In the interval $\left[0, \frac{\pi}{2}\right]$, find the area of the region bounded by the curve $y =\cos x$ and the $x$-axis.

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Q 101 Marks Question1 Mark

Find the area bounded by the curve $y=x$, the $x$-axis and the ordinates $x=0$ and $x=a$.

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Q 112 Marks Questions2 Marks

Find the area of the region bounded by the curve $y^2=9 x, x=2, x=4$ and the $x-$axis in the first quadrant.

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Q 122 Marks Questions2 Marks

Find the area of the region bounded by the parabola $y^2=4 a x$ and its latus rectum.

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Q 132 Marks Questions2 Marks

Find the area of the region bounded by $y=x$, the $x$-axis, $x=-1$ and $x=2$.

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Q 142 Marks Questions2 Marks

Find the area of the region bounded by $y=|x|$, $x =-3, x =1$ and the $x-$axis.

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Q 152 Marks Questions2 Marks

Find the area bounded by the curve $y=x^3-6 x^2+$ $8 x, x=a, x=b$ and the $x$-axis.

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Q 163 Marks Question3 Marks

Find the area enclosed by the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$. Draw the figure.

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Q 173 Marks Question3 Marks

Find the area of the region bounded by the curve $y=\sin 2 x+\cos 2 x$ and $x=0$ and $x=\frac{\pi}{4}$.

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Q 18Fill In The Blanks[1 Marks ]1 Mark

The area between the curve $y^2=4 a x$, line $y=2 a$ and $y$-axis will be ____________.

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Q 19Fill In The Blanks[1 Marks ]1 Mark

The area enclosed by the $\frac{x^2}{36}+\frac{y^2}{16}=1$ will be ____________ .

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Q 20Fill In The Blanks[1 Marks ]1 Mark

The area bounded by the curve $y=\sec x, x=0$ and $x=2 \pi$ the $x$-axis will be __________ .

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Q 21Fill In The Blanks[1 Marks ]1 Mark

The area bounded by the curve $y=\sin x^2, x=1, x=2$ and the $x$-axis will be ____________ .

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Q 22Fill In The Blanks[1 Marks ]1 Mark

In the first quadrant the area of the region bounded by the circle $x^2+y^2=(2)^2$ and lines $x=0, x=2$ will be ___________ .

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Application of Integrals Maths - Application of Integrals

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