Evaluate : (\integral\_{0}^{\pi/2}{\sin^{9}x})cos4 x dx - | MATH - FUNDAMENTAL DEFINITE INTEGRATION, DEFINITE INTEGRATION BY SUBSTITUTION | SolveeIt

Evaluate : $\int_{0}^{\pi/2}{\sin^{9}x}$ cos⁴ x dx -

$\frac{128}{1515}$

$\frac{128}{15015}$

$\frac{64}{15015}$

None of these

Answer

$\frac{128}{15015}$

Explanation

Let I = $\int_{0}^{\pi/2}{\sin^{9}x}$ cos⁴x dx

= $\frac { ( 8.6 .4 .2 ) ( 3.1 ) } { ( 13.11 .9 .7 .5 .3 .1 ) }$ . 1 (from walli's formula)

= $\frac { 128 } { 15015 }$ .

Question: Evaluate : \(\int_{0}^{\pi/2}{\sin^{9}x}\)cos<sup>4</sup> x dx -...