Mathematics

$I_n = \int^x_0 e^x (sin x)^n dx$ , then $\dfrac{I_3}{I_1}$ is equal to

$\dfrac{3}{5}$

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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 value of $\displaystyle\int_{-\frac{\pi }{2}}^{\frac{\pi}{2}} {\dfrac{{{{\sin }^2}x}}{{1 + {2^x}}}dx}$ is $:$
• A. $4\pi$
• B. $\dfrac{\pi }{8}$
• C. $\dfrac{\pi }{2}$
• D. $\dfrac{\pi }{4}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Solve $\displaystyle\int \dfrac{x}{{{{\left( {x + 1} \right)}^2}}}dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
Evaluate: $\displaystyle \int e^{x}\sin \left ( e^{x} \right )dx$
• A. $\displaystyle \cos e^{x}+C$
• B. $\displaystyle \left ( \cos e^{x} \right )^{-1}+C$
• C. $\displaystyle \sin e^{x}+C$
• D. $\displaystyle -\cos e^{x}+C$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate: $\displaystyle\int {{{\cos 2x} \over {\sin x}}dx}$

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