Question

The area bounded by the curve $y=x^3,y=-1,y=8$ and y-axis is

• A. $\frac{45}{4}$
• B. $\frac{4}{45}$
• C. $\frac{51}{4}$
• D. $\frac{47}{4}$

Answer 1

Answer: (C)

$\frac{51}{4}$

REF.Image.

Area $=|{\int }_{-1}^0{y}^{1/3}dy|$ +$|{\int }_0^8{y}^{1/3}dy|$

$=|\frac{3}{4}[y^{4/3}{]}_{-1}^0|+|\frac{3}{4}[y^{4/3}{]}_0^8$

$=\frac{3}{4}+\frac{3}{4}{8}^{4/3}$

$=\frac{3}{4}(1+2^3\times \frac{4}{3})$

$=\frac{3}{4}(1+16)=\frac{17\times 3}{4}=\frac{51}{4}$