Application of Integrals: 1 mark Questions (CBSE Class 12)

The area bounded by the curve $y=x|x|$, $x$-axis and the ordinates $x=-1$ and $x=1$ is given by

1. (A)0
2. (B)$\frac{1}{3}$
3. (C)$\frac{2}{3}$
4. (D)$\frac{4}{3}$

Which of the following expressions will give the area of region bounded by the curve $y=x^2$ and line $y=16$ ?

1. (A)${\int }_0^4{x}^{2}dx$
2. (B)$2{\int }_0^4{x}^{2}dx$
3. (C)${\int }_0^{16}\sqrt{y}dy$
4. (D)$2{\int }_0^{16}\sqrt{y}dy$

The area of the shaded region of the circle given below is equal to :

1. (A)${\int }_1^3\sqrt{9-y^2}dy$
2. (B)$2{\int }_1^3\sqrt{9-y^2}dy$
3. (C)${\int }_0^3\sqrt{9-x^2}dx$
4. (D)$2{\int }_0^3\sqrt{9-x^2}dx$

The area of the region bounded by the curve y = x and x-axis, between x = 0 and x = 2 is :

1. (A)2 sq. units
2. (B)$\frac{1}{2}$ sq. unit
3. (C)1 sq. unit
4. (D)4 sq. units

An ant is observed crawling on a sheet of paper along a straight line given by equation $y=2x-4$. Area of the surface covered by the ant bounded by y-axis, x-axis and $x=1$ is :

1. (A)1 sq. unit
2. (B)3 sq. units
3. (C)2 sq. units
4. (D)4 sq. units