Mathematics

# $\displaystyle \int _{}{ \sin ^{ 8 }{ x } \cos ^{ }{ x } dx }$

##### SOLUTION
Let $\sin x=t\implies \cos dx=dt$
$\displaystyle \int t^8dt\\\dfrac{t^9}{9}+c\\\dfrac{\sin ^9t}{9}+c$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 105

#### Realted Questions

Q1 Single Correct Medium
What is $\int_ {-\frac{\pi}{2}}^{\frac{\pi}{2}} x \, sin \, x dx$equal to ?
• A.
• B. -2
• C. $\pi$
• D. 2

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\int_{0}^{\pi /2}sin2xtan^{-1}\left ( sinx \right )dx=$

• A.  $\dfrac{\pi }{2}$+1
• B.  $\dfrac{3\pi }{2}$+1
• C.  $\dfrac{3\pi }{2}$-1
• D.  $\dfrac{\pi }{2}$-1

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\displaystyle\int^{\dfrac{\pi}{4}}_{\dfrac{-\pi}{4}}\sqrt{\dfrac{1-\cos 2008x}{2}}dx$ equals?
• A. $\dfrac{1}{251}$
• B. $\dfrac{1}{498}$
• C. $\dfrac{1}{502}$
• D. $\dfrac{1}{249}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
a) Prove that $\overset { a }{ \underset { 0 }{ \int } }f(x)dx = \overset { a }{ \underset { 0 }{ \int } }f(a-x). dx$ and hence evaluate
$\overset { \pi /4 }{ \underset { 0 }{ \int } }\log (1+\tan x) dx$
b) Find the value of $k$, if
$f(x)=\begin{cases}\dfrac{k \cos x}{\pi - 2x}&if x \ne \dfrac{\pi}{2}\\3& if x = \dfrac{\pi}{2}\end{cases}$
is continuous at $x=\dfrac{\pi}{2}$.

$\displaystyle\int^{\dfrac{\pi}{2}}_0\dfrac{\sin x}{1+\cos^2x}dx$.