Mathematics

# $\int { { (cosx) }^{ 4 } } dx=Ax+Bsin2x+Csin4x$ then {A,B,C) equals

$\left\{ \frac { 3 }{ 8 } ,\frac { 1 }{ 4 } ,\frac { 1 }{ 32 } \right\}$

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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 Hard
Evaluate : $\int^1_0$$\frac{log (1 +x)}{1 + x^2}dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
If $\displaystyle \int \frac{dx}{\left ( x-p \right )\sqrt{\left ( x-p \right )\left ( x-q \right )}} \displaystyle =-\frac{2}{p-q}\sqrt{\frac{x-a}{x-b}}+c$ then find $a$ and $b$ are respectively
• A. $p,q$
• B. $q,q^2$
• C. $p^2,q^2$
• D. $q,p$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
$\text { Evaluate: } \displaystyle \int e^{x}\left(\dfrac{\sin 4 x-4}{1-\cos 4 x}\right) d x$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium

$\displaystyle \int_{0}^{\frac{\pi}{2}}\frac{f(\sin x)}{f(\sin x)+f(\cos x)}dx=$
• A. $\pi$
• B. $2\pi$
• C. $\dfrac {\pi}{2}$
• D. $\dfrac {\pi}{4}$

Given that for each $\displaystyle a \in (0, 1), \lim_{h \rightarrow 0^+} \int_h^{1-h} t^{-a} (1 -t)^{a-1}dt$ exists. Let this limit be $g(a)$
In addition, it is given that the function $g(a)$ is differentiable on $(0, 1)$