Mathematics

# If $\int_{0}^{1} e^{x^{2}}(x-\alpha) d x=0,$ then

$1<\alpha<2$

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

#### Realted Questions

Q1 Subjective Medium
Evaluate $\int _{ -1 }^{ 3 }{ \left| { x }^{ 2 }-1 \right| dx }$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Let $f(x)=x+\phi(x)$ where $\phi(x)$ is an even function then find the value of $\displaystyle\int_{-1}^{1}xf(x)\ dx$.

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
$\displaystyle\int^2_1\left(\dfrac{1}{x}-\dfrac{1}{2x^2}\right)e^{2x}dx$.

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
The value of $\displaystyle \int_{-\pi }^{\pi }\displaystyle \frac{\cos ^{2}x}{1+a^{x}}\: dx,a> 0$ is
• A. $a\pi$
• B. $\pi$
• C. $2\pi$
• D. $\pi /2$

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