Mathematics

$\displaystyle \overset{\pi/2}{\underset{0}{\int}} \dfrac{4 + 3 \sin x}{4 + 3 \cos x} dx$

$1$

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 Single Correct Medium
$\displaystyle \int_{0}^{\frac {\pi}{2}} \dfrac {\sin x - \cos x}{1 + \sin x \cdot \cos x} dx$ is equal to
• A. $\dfrac {\pi}{4}$
• B. $\dfrac {\pi}{2}$
• C. $\pi$
• D. $0$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Evaluate $\displaystyle \int \frac{1}{(x-1)(x^{2}+1)}dx$
• A. $\displaystyle \frac{1}{2}log(x-1)+\frac{1}{4}log(x^{2}+1)-\frac{1}{2}\tan ^{-1}x+c$
• B. $\displaystyle \frac{1}{2}log(x-1)-\frac{1}{2}log(x^{2}+1)-\frac{1}{2}\tan ^{-1}x+c$
• C. $\displaystyle \frac{1}{2}log(x-1)-\frac{1}{4}log(x^{2}+1)+\tan ^{-1}x+c$
• D. $\displaystyle \frac{1}{2}log(x-1)-\frac{1}{4}log(x^{2}+1)-\frac{1}{2}\tan ^{-1}x+c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
$\displaystyle\int_{0}^{2}x\sqrt{x+2}dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate $\displaystyle \int \dfrac{\cot x}{\sqrt{\sin x}}dx$

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