Mathematics

# If $f\left( 8-t \right) =f(t)$ and $\int _{ 0 }^{ 4 }{ f(\alpha ) } d\alpha =8$, then $\int _{ 0 }^{ 8 }{ f(\gamma ) } d\gamma$ is

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

#### Realted Questions

Q1 Single Correct Medium
The integral $\displaystyle \int \dfrac{x+2}{(x^{2}+3x+3)\sqrt{x+1}}\ dx$ is equal to :
• A. $\dfrac{2}{\sqrt{3}}\tan^{-1}{\left[\dfrac{x}{\sqrt{3(x+1)}}\right] }+C$
• B. $\dfrac{2}{\sqrt{3}}\cot^{-1}{\left[\dfrac{x}{\sqrt{3(x+1)}}\right] }+C$
• C. $none\ of\ these$
• D. $\dfrac{1}{\sqrt{3}}\tan^{-1}{\left[\dfrac{x}{\sqrt{3(x+1)}}\right] }+C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
If $\int\dfrac{1}{x\sqrt{1 - x^3}}dx = a \,log \left|\dfrac{\sqrt{1 - x^3}- 1}{\sqrt{1 - x^2}+ 1}\right| + b$ then $a =$
• A. $\dfrac{2}{3}$
• B. $-\dfrac{2}{3}$
• C. $-\dfrac{1}{3}$
• D. $\dfrac{1}{3}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Solve:
$\int \dfrac { \cos 2x + 2 \sin^2 x }{ \cos^2 x } dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
If $\displaystyle I=\int \frac{5x^{8}+7x^{6}}{\left ( x^{2}+1+2x^{7} \right )^{2}}dx$ then $I$ is equal to
• A. $\displaystyle \frac{x^{2}}{2x^{2}+x^{2}+1}+C$
• B. $\displaystyle \frac{x^{5}}{x^{2}+1+2x^{7}}+C$
• C. $\displaystyle \frac{-1}{2x^{7}+x^{2}+1}+C$
• D. $\displaystyle \frac{p\left ( X \right )}{q\left ( x \right )}, deg$ p(x)$=deg$ q(x)$=7$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
The absolute value of $\displaystyle \int_{10}^{19}\dfrac {\sin x}{1+x^{8}}$ is less than:
• A. $10^{-11}$
• B. $10^{-7}$
• C. $10^{-9}$
• D. $10^{-10}$