Mathematics

# The value of $\int_{0}^{\pi /2}\frac{dx}{1+tan^{3}x}$ is

Its FREE, you're just one step away

Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 One Word Hard
If $\displaystyle 2f(x) + f(-x) = \displaystyle \frac {1}{x} \sin (x - \frac {1}{x})$, then the value of $\displaystyle I = \int_{1/e}^{e} f(x)dx$ is equal to

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle\int {{{dx} \over {\sqrt {{{\sin }^3}x\cos x} }} = g(x)} + c \Rightarrow g(x) =$
• A. $\displaystyle{2 \over {\sqrt {\cot x} }}$
• B. $\displaystyle{2 \over {\sqrt {\tan x} }}$
• C. $\displaystyle{1 \over {\sqrt {\cot x} }}$
• D. $\displaystyle{{ - 2} \over {\sqrt {\tan x} }}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
$\displaystyle\int_{0}^{\pi/2}\dfrac{\cos^{2}x}{1+3\sin^{2}x}\ dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Integrate $\displaystyle \int \dfrac{1}{x^{2/3}\sqrt{x^{2/3}-4}}dx$

Let $\displaystyle f\left ( x \right )=\frac{\sin 2x \cdot \sin \left ( \dfrac{\pi }{2}\cos x \right )}{2x-\pi }$