Mathematics

# Evaluate: $\displaystyle \int {{\dfrac{\cos 2x - \cos 2\alpha }{\cos x - \cos \alpha }}} dx$

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

#### Realted Questions

Q1 Subjective Hard
Evaluate $\displaystyle \int { \dfrac { \left( \cos { 5x+\cos { 4x } } \right) }{ 1-2\cos { 3x } } } dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle\int \frac{x}{\sqrt{\left ( 4-x^{4} \right )}}dx$
• A. $\displaystyle \sin ^{-1}\left ( \frac{1}{2}x^{2} \right ).$
• B. $\displaystyle \frac{1}{2}\sin ^{-1}\left ( x^{2} \right ).$
• C. $\displaystyle \frac{1}{2}\cos ^{-1}\left ( \frac{1}{2}x^{2} \right ).$
• D. $\displaystyle \frac{1}{2}\sin ^{-1}\left ( \frac{1}{2}x^{2} \right ).$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate the following integral:
$\displaystyle\int^a_0\dfrac{x}{\sqrt{a^2+x^2}}dx$.

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate the following integrals
$\displaystyle\int {\dfrac{{{x^2}}}{{{{\left( {{a^2} - {x^2}} \right)}^{3/2}}}}dx}$

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