NDA 2024 Maths · Mathematics · Application of Integrals · hard

The total area enclosed between the curve y=x^3, the x-axis and the lines x=-1 and x=2 is

Single correct option

The total area enclosed between the curve

y=x^3

, the

x

-axis and the lines

x=-1

and

x=2

Show answer and solution

Answer: (D) $\frac{17}{4}$ square units

The curve lies below the axis for

-1<x<0

and above it for

0<x<2

, so the area is the sum of absolute values:

\left|\int_{-1}^0x^3dx\right|+\int_0^2x^3dx=\frac14+4=\frac{17}{4}

. Trap: integrating straight through gives the signed value

\frac{15}{4}

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