Mathematics

# The value of ${\int}_{0}^{\pi}\left|\sin^{4}x\right|dx$ is

$\dfrac{8\pi}{3}$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Subjective Medium
$y=\displaystyle\int \dfrac{\cos x}{1+\sin x}dx$.

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\int _ { - 3 \pi / 2 } ^ { - \pi / 2 }\left( ( x + \pi ) ^ { 3 } + \cos ^ { 2 } ( x + 3 \pi ) \right] d x$  is equal to-
• A. $\left( x ^ { 4 } / 32 \right) + ( \pi / 2 )$
• B. $( \pi / 4 ) - 1$
• C. $\pi ^ { 4 } / 32$
• D. $\pi / 2$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
The integral $\int \dfrac {dx}{(1 + \sqrt {x})\sqrt {x - x^{2}}}$ is equal to (where C is a constant of integration):
• A. $-2\sqrt {\dfrac {1 + \sqrt {x}}{1 - \sqrt {x}}} + C$
• B. $-\sqrt {\dfrac {1 - \sqrt {x}}{1 + \sqrt {x}}} + C$
• C. $2\sqrt {\dfrac {1 + \sqrt {x}}{1 - \sqrt {x}}} + C$
• D. $-2\sqrt {\dfrac {1 - \sqrt {x}}{1 + \sqrt {x}}} + C$

1 Verified Answer | Published on 17th 09, 2020

Q4 One Word Medium
Evaluate the following integrals:$\displaystyle \sqrt{x^{2}+6x-4} dx$

Let $F: R\rightarrow R$ be a thrice differential function. Suppose that $F(1) = 0, F(3) = -4$ and $F'(x)<0$ for all $x\in\left(\dfrac{1}{2},3\right)$. Let $f(x) = xF(x)$ for all $x\in R$.