Question

Area bounded by the curve y = x³, the x–axis and the ordinates x = −2 and x = 1 is

(A) −9

(B) \(- \frac{15}4\)

(C) \(\frac{15}4\)

(D) \(\frac{17}4\)

Answer 1

Correct option is (D) \(\frac{17}4\)

Required area = \(- \int\limits_{-2}^0x^3dx + \int\limits_0^1x^3dx\)

\(=-\left[\frac{x^4}4\right]_{-2}^0 + \left[\frac{x^4}4\right]_{0}^1\)

\(= -\left[0 - \frac{(-2)^4}4\right] + \frac14\)

\(= \left(\frac14 + 4\right)\)

\(= \frac{17}4\) sq. units