Area bounded by y = x3, y = 8 and x = 0 is

Question

Area bounded by y = x3, y = 8 and x = 0 is (A) 11 sq. units (B) 14 sq. units (C) 12 sq. units (D) 6 sq. units

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/8ebd1c5092e8d69bd690850c39ca76c3-.png" /> Required area =∫ limits08 x d y =∫ limits08 y1 / 3 d y =(3/4)[y4 / 3]08=(3/4)(84 / 3) =(3/4) × 16=12 sq units

Q. Area bounded by $y = x^{3}, y = 8$ and $x = 0$ is

$11$ sq. units

$14$ sq. units

$12$ sq. units

$6$ sq. units

Required area $= 0 \int 8 x d y$
$= 0 \int 8 y^{1/3} d y$
$= \frac{3}{4} [y^{4/3}]_{0}^{8} = \frac{3}{4} (8^{4/3})$
$= \frac{3}{4} \times 16 = 12$ sq units

Q. Area bounded by y=x3,y=8 and x=0 is

11 sq. units

14 sq. units

12 sq. units

6 sq. units