The area bounded by the curve y = x2 , the y -axis and the straight lines y = 1 and y = 4 is

Question

The area bounded by the curve y = x2 , the y -axis and the straight lines y = 1 and y = 4 is (A)  (14/3) sq. units (B)  (11/3) sq. units (C)  (14/5) sq. units (D)  (1/3) sq. units

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/ff68ba95b0e0733caaf23671e1f47485-.png" /> Required area = ∫14 √y dy = [(2y3/2/3)]14 = (2/3)[8-1] = (14/3) sq. units

Q. The area bounded by the curve $y = x^{2}$ , the $y$ -axis and the straight lines $y = 1$ and $y = 4$ is

$\frac{14}{3}$ sq. units

$\frac{11}{3}$ sq. units

$\frac{14}{5}$ sq. units

$\frac{1}{3}$ sq. units

Required area
$= \int_{1}^{4} y d y = [\frac{2 y ^{3/2}}{3}]_{1}^{4}$
$= \frac{2}{3} [8 - 1] = \frac{14}{3}$ sq. units

Q. The area bounded by the curve y=x2 , the y -axis and the straight lines y=1 and y=4 is

314​ sq. units

311​ sq. units

514​ sq. units

31​ sq. units