Mathematics

# The integral $\displaystyle \int_{0}^{\pi} \sqrt{1+4sin^2\dfrac{x}{2}-4sin\dfrac{x}{2}}dx$ is equal to

$4\sqrt{3}-4-\dfrac{\pi}{3}$

##### SOLUTION
Hence, Option (D) is the correct option Its FREE, you're just one step away

Single Correct Hard Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 105

#### Realted Questions

Q1 Subjective Medium
If $I=\displaystyle \int_{0}^{\pi/2}sinx.log(sin x)dx = log\left(\dfrac{K}{e}\right).$ Then find the value of $K.$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Evaluate: $\displaystyle \int_{0}^{2\pi}e^{x/2}\ \sin \left ( \frac{1}{2}x+\frac{\pi }{4} \right ) dx$
• A. $2\sqrt{2}$
• B. $2 \pi$
• C. $e^{\pi}$
• D. $0$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
The value of $\displaystyle \int \frac{(ax^{2}-b)dx}{x\sqrt{c^{2}x^{2}-(ax^{2}+b)^{2}}}$ is equal to
• A. $\displaystyle \frac{1}{c}\sin^{-1}\left ( ax+\frac{b}{x} \right )+k$
• B. $\displaystyle c\sin^{-1}\left ( a+\frac{b}{x} \right )+k$
• C. none of these
• D. $\displaystyle \sin^{-1}\left ( \frac{ax+\frac{b}{x}}{c} \right )+k$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate $\displaystyle \int_{0}^{\pi /2}\cos x\ dx$

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 $\displaystyle f(x)>0 \forall x \in R$