Mathematics

# Evaluate:$\displaystyle \int \frac{dx}{\sqrt{16-x^{2}}}$

$sin^{-1}\dfrac{x}{4}+C$

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

#### Realted Questions

Q1 Single Correct Medium
Evaluate:$\displaystyle \int \frac{(2x-3)}{(x^{2}+3x-18)}dx$
• A. $\dfrac12 \log\left | x^{2}+3x-18 \right |-\dfrac{2}{3} \log\left | \dfrac{x-3}{x+6} \right |+C$
• B. $\log\left | x^{2}+3x-18 \right |-\dfrac{1}{3} \log\left | \dfrac{x-3}{x+6} \right |+C$
• C. none of these
• D. $\log\left | x^{2}+3x-18 \right |-\dfrac{2}{3} \log\left | \dfrac{x-3}{x+6} \right |+C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
Integrate the function    $\cfrac {x+3}{x^2-2x-5}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate $\displaystyle\int^{\pi/2}_0\cos^4xdx$.

1 Verified Answer | Published on 17th 09, 2020

Q4 One Word Medium
Evaluate :
$\displaystyle{\int_{0}^{\pi}{\frac{x tan x}{sec x + tan x}}}$

Consider two differentiable functions $f(x), g(x)$ satisfying $\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$ & $\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$. where $\displaystyle f(x)>0 \forall x \in R$