Intergreeting Integrals #4

Calculus Level 3

Evaluate $\displaystyle \int x^2.cos(x^3)\sqrt{sin^{7}(x^{3})}dx$

\dfrac{1}{9}[sin(x^{2})]^\frac{7}{2}+c

\dfrac{2}{27}[sin(x^{3})]^\frac{9}{2}+c

\text{None of these}

\dfrac{2}{27}[cos(x^{3})]^\frac{1}{2}+c

\text{Not defined}

logx+c

1 solution

Lu Chee Ket
Jan 29, 2015

Let u = Sin x^3

d u = 3 x^2 Cos x^3 d x

(1/ 3) Integrate u^(7/ 2) d u = (2/ 27) u^(9/ 2) + C = (2/ 27)(Sin x^3)^(9/ 2) + C