(A) Area bounded by region 0 ≤ y ≤ 4 x - x 2 - 3 is (p) 32 3 (B) The area of figure formed by all the points satisfying the inequality y 2 ≤ 4 1 - x is (q) 1 2 (C) The area bounded by x + y ≤ 1 and x ≥ 1 / 2 is (r) 4 3 (D) Area bounded by x ≤ 4 - y 2 and x ≥ 0 is (s) 16 3

a We have, 0 ≤ y ≤ 4 x - x 2 - 3 Required area = ∫ 1 3 4 x - x 2 - 3 d x = 2 x 2 - x 3 3 - 3 x 1 3 = 18 - 9 - 9 - 2 - 1 3 - 3 = 4 3 sq . units b We have y 2 ≤ 4 1 - x Required area = 4 ∫ 0 2 1 - y 2 4 d y = 4 y - y 3 12 0 2 = 4 2 - 2 3 = 16 3 sq . units c We have x + y ≤ 1 . . . i x ≥ 1 2 . . . ii Required Area = 4 × ∫ 1 / 2 1 1 - x d x = 4 × x - x 2 2 1 / 2 1 = 4 × 1 - 1 2 - 1 2 - 1 8 = 1 2 sq . units d We have x ≤ 4 - y 2 . . . i x ≥ 0 . . . ii Required area = ∫ - 2 2 4 - y 2 d y = 2 × ∫ 0 2 4 - y 2 d y = 2 × 4 y - y 3 3 0 2 = 2 × 8 - 8 3 = 32 3 sq . units

E M B I B E

Alpha Question Bank for Engineering: Mathematics>Chapter 31 - Area under Curves>Exercise-1>Q 12

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The area bounded by $x$ -axis and the curve $y = 4 x - x^{2} - 3$ is

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Important Questions on Area under Curves

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JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 31 - Area under Curves>Exercise-1>Q 13

The area of the figure bounded by right of the line

y = x + 1, y = \cos x

and

x

-axis is

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Alpha Question Bank for Engineering: Mathematics>Chapter 31 - Area under Curves>Exercise-1>Q 14

Area bounded by curve

y^{3} - 9 y + x = 0

and

y

-axis is

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Alpha Question Bank for Engineering: Mathematics>Chapter 31 - Area under Curves>Exercise-1>Q 16

The area bounded by

y = 2 - |2 - x|

and

y = \frac{3}{|x|}

is

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 31 - Area under Curves>Exercise-1>Q 18

Area of region bounded by

x = 0, y = 0, x = 2, y = 2,

y \leq e^{x}

and

y \geq \ln x

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 31 - Area under Curves>Exercise-1>Q 20

The area bounded by the parabolas

y = (x + 1)^{2}

and

y = (x - 1)^{2}

and the line

y = 1 / 4

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 31 - Area under Curves>Exercise-1>Q 21

(A)	Area bounded by region $0 \leq y \leq 4 x - x^{2} - 3$ is	(p)	$\frac{32}{3}$
(B)	The area of figure formed by all the points satisfying the inequality $y^{2} \leq 4 (1 - \|x\|)$ is	(q)	$\frac{1}{2}$
(C)	The area bounded by $\|x\| + \|y\| \leq 1$ and $\|x\| \geq 1 / 2$ is	(r)	$\frac{4}{3}$
(D)	Area bounded by $x \leq 4 - y^{2}$ and $x \geq 0$ is	(s)	$\frac{16}{3}$