Mathematics

# If $\int x^2 . e^{-2x} dx=e^{-2x}(ax^2+bx+c)+d,$ then

$a=\dfrac12,b=\dfrac12,c=\dfrac{1}{4}$

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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 Hard
$\displaystyle \int\frac{\mathrm{x}^{2}-1}{\mathrm{x}^{3}\sqrt{2\mathrm{x}^{4}-2\mathrm{x}^{2}+1}}$ dx is equal to

• A. $\displaystyle \frac{\sqrt{2\mathrm{x}^{4}-2\mathrm{x}^{2}+1}}{\mathrm{x}^{2}}+\mathrm{c}$
• B. $\displaystyle \frac{\sqrt{2\mathrm{x}^{4}-2\mathrm{x}^{2}+1}}{\mathrm{x}^{3}}+\mathrm{c}$
• C. $\displaystyle \frac{\sqrt{2\mathrm{x}^{4}-2\mathrm{x}^{2}+1}}{\mathrm{x}}+\mathrm{c}$
• D. $\displaystyle \frac{\sqrt{2\mathrm{x}^{4}-2\mathrm{x}^{2}+1}}{2\mathrm{x}^{2}}+\mathrm{c}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate $\displaystyle \int \dfrac{1}{(a^2-x^2)^{\tfrac 3 2}}dx$.

1 Verified Answer | Published on 17th 09, 2020

Q3 One Word Medium
Evaluate:$\displaystyle \int \frac{dx}{\sqrt{9+4x^{2}}}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Evaluate : $\displaystyle \int \dfrac { 1 - x ^ { 7 } } { x \left( 1 + x ^ { 7 } \right) } d x$

1 Verified Answer | Published on 17th 09, 2020

Q5 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. $1-\dfrac {\pi}{4}$