Mathematics

# If $\frac { d } { d x } f ( x ) = g ( x )$ then the value of $\int _ { a } ^ { b } f ( x ) g ( x ) d x$ is

$\frac { 1 } { 2 } \left[ \{ g ( b ) \} ^ { 2 } - \{ g ( a ) \} ^ { 2 } \right]$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Single Correct Medium
$\int_{0}^{\pi/4}\tan^{2}\ x\ dx$
• A. $\dfrac {\pi}{4}$
• B. $1+\dfrac {\pi}{4}$
• C. $1-\dfrac {\pi}{2}$
• D. $1-\dfrac {\pi}{4}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate $\displaystyle\int_{1}^{4} (x-1)\ dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Assertion & Reason Hard
##### ASSERTION

$\displaystyle \int \frac{xe^{x}}{\left ( 1+x \right )^{2}}dx=\frac{e^{x}}{1+x}+C$

##### REASON

$\int e^{x}\left ( f\left ( x \right )+{f}'\left ( x \right ) \right )dx=e^{x}f\left ( x \right )+C$

• A. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• B. Assertion is correct but Reason is incorrect
• C. Both Assertion and Reason are incorrect
• D. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
The value of $\displaystyle\int_{-1}^{1}\log \left (\dfrac {x - 1}{x + 1}\right )dx$ is
• A. $1$
• B. $2$
• C. $4$
• D. $0$

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