Class 12

Math

Calculus

Application of Integrals

Area bounded by the curve $y=x_{3}$, the x-axis and the ordinates $x=2$and $x=1$is(A) $−9$ (B) $4−15 $ (C) $415 $ (D) $417 $

As per diagram, required area will be,

$∫_{−2}x_{3}dx+∫_{0}x_{3}dx$

$=∣∣ 4x_{4} ∣∣ _{−2}+∣∣ 4x_{4} ∣∣ _{0}$

$=416 +41 =417 $, which is the required area.