Application of Integrals
Free NCERT & Exemplar step-by-step solutions — CBSE Class 12 Mathematics
NCERT Exemplar
• $\sqrt 2$ sq units
• $(\sqrt 2 + 1)$ sq units
• $(\sqrt 2 - 1)$ sq units
• $(2\sqrt 2 - 1)$ sq units
Correct Option (c)
LA Q25 The area of the region bounded by the curve ${x^2} = 4y$ and the straight line $x = 4y - 2$ is• $\frac{3}{8}$ sq units
• $\frac{5}{8}$ sq units
• $\frac{7}{8}$ sq units
• $\frac{9}{8}$ sq units
LA Q26 The area of the region bounded by the curve $y = \sqrt {16 - {x^2}}$ and $x$ -axis is• 8 sq units
• $20\pi$ sq units
• $16\pi$ sq units
• $256\pi$ sq units
Correct Option (a)
LA Q27 Area of the region in the first quadrant enclosed by the $x$ -axis, the line $y = x$ and the circle ${x^2} + {y^2} = 32$ is• $16\pi$ sq units
• $4\pi$ sq units
• $32\pi$ sq units
• 24 sq units
Correct Option (b)
LA Q28 Area of the region bounded by the curve $y = \cos x$ between $x = 0$ and $x = \pi$ is• 2 sq units
• 4 sq units
• 3 sq units
• 1 sq units
Correct Option (a)
LA Q29 The area of the region bounded by parabola ${y^2} = x$ and the straight line $2y = x$ is• $\frac{4}{3}$ sq units
• 1 sq units
• $\frac{2}{3}$ sq units
• $\frac{1}{3}$ sq units
Correct Option (a)
LA Q30 The area of the region bounded by the curve $y = \sin x$ between the ordinates $x = 0$, $x = \frac{\pi }{2}$ and the $x$ -axis is• 2 sq units
• 4 sq units
• 3 sq units
• 1 sq units
Correct Option (d)
LA Q31 The area of the region bounded by the ellipse $\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{{16}} = 1$ is• $20\pi$ sq units
• $20{\pi ^2}$ sq units
• $16{\pi ^2}$ sq units
• $25\pi$ sq units
Correct Option (a)
LA Q32 The area of the region bounded by the circle ${x^2} + {y^2} = 1$ is• $2\pi$ sq units
• $\pi$ sq units
• $3\pi$ sq units
• $4\pi$ sq units
Correct Option (b)
LA Q33 . The area of the region bounded by the curve $y = x + 1$ and the lines $x = 2$ and $x = 3$ is• $\frac{7}{2}$ sq units
• $\frac{9}{2}$ sq units
• $\frac{{11}}{2}$ sq units
• $\frac{{13}}{2}$ sq units
Correct Option (a)
LA Q34 The area of the region bounded by the curve $x = 2y + 3$ and the $y$ lines. $y = 1$ and $y = - 1$ is• 4 sq units
• $\frac{3}{2}$ sq units
• 6 sq units
• 8 sq units
Correct Option (c)
LA Q1 Find the area of the region bounded by the curves ${y^2} = 9x$, $y = 3x$. SA Q2 Find the area of the region bounded by the parabola ${y^2} = 2px$, ${x^2} = 2py$. SA Q3 Find the area of the region bounded by the curve $y = {x^3}$ and $y = x + 6$ and $x = 0$. SA Q4 Find the area of the region bounded by the curve ${y^2} = 4x$, ${x^2} = 4y$. SA Q5 Find the area of the region included between ${y^2} = 9x$ and $y = x$. SA Q6 Find the area of the region enclosed by the parabola ${x^2} = y$ and the line $y = x + 2$. SA Q7 Find the area of region bounded by the line $x = 2$ and the parabola ${y^2} = 8x$ SA Q8 Sketch the region $\left\{ {(x,0):y = \sqrt {4 - {x^2}} } \right\}$ and $x$ -axis. Find the area of the region using integration. SA Q9 Calcualte the area under the curve $y = 2\sqrt x$ included between the lines $x = 0$ and $x = 1$. SA Q10 Using integration, find the area of the region bounded by the line $2y = 5x + 7,x$ axis and the lines $x = 2$ and $x = 8$. SA Q11 Draw a rough sketch of the curve $y = \sqrt {x - 1}$ in the interval [1,5] . Find thearea under the curve and between the lines $x = 1$ and $x = 5$. SA Q12 Determine the area under the curve $y = \sqrt {{a^2} - {x^2}}$ included between the lines $x$ $= 0$ and $x = a$. SA Q13 Find the area of the region bounded by $y = \sqrt x$ and $y = x$. SA Q14 Find the area enclosed by the curve $y = - {x^2}$ and the straight lilne $x + y + 2 = 0$. SA Q15 Find the area bounded by the curve $y = \sqrt x$, $x = 2y + 3$ in the first quadrant and $x$-axis. SA