Question

Find the area of the curve $y=4x^3$ between the end points $x=[-2,3]$

• (A) 97
• (B) 65
• (C) 70
• (D) 77

Answer 1

The Correct Option is A

Explanation:
Let $f(x)=y=4x^3$Given the end points are: ${\mathrm{x}}_1=-2,{\mathrm{x}}_2=3$Therefore, Area of the curve $(A)=\left|{\int }_{-2}^{3}4x^3\mathrm{dx}\right|$$\Rightarrow \mathrm{A}=\left|{\int }_{-2}^{0}4{\mathrm{x}}^3\mathrm{d}\mathrm{x}\right|+\left|{\int }_0^{3}4{\mathrm{x}}^3\mathrm{dx}\right|$$\Rightarrow \mathrm{A}=\left|4{\left[\frac{{\mathrm{x}}^4}{4}\right]}_{-2}^0\right|+\left|4{\left[\frac{{\mathrm{x}}^4}{4}\right]}_0^3\right|$$\Rightarrow \mathrm{A}=\left|[0-2^4]\right|+\left|[3^4-0]\right|$$\Rightarrow \mathrm{A}=|-16|+|81|$$\Rightarrow \mathrm{A}=97$Hence, the correct option is (A).