Mathematics

# Evaluate : $\int _ { - \pi } ^ { \pi } ( \cos a x - \sin b x ) ^ { 2 } d x$

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

#### Realted Questions

Q1 Multiple Correct Hard
Let $\displaystyle \alpha +\beta =1,2\alpha ^{2}+2\beta ^{2}=1$ and f(x) be a continuous function such that f(x + 2) + f(x) = 2 $\displaystyle \forall \times \epsilon \left [ 0,2 \right ]\: \: and\: \: \left ( p+4 \right )=\int_{0}^{4}f\left ( x \right )dx\: \&\: q=\frac{\alpha }{\beta }$ exactly one root of the equation $\displaystyle ax^{2}-bx+c=0$ is lying between p and q when a, b, $\displaystyle c\: \epsilon \: N$ then
• A. $\displaystyle b^{2}-4ac\leq 0$
• B.
$c(a - b + c) > 0$
• C. $\displaystyle b^{2}-4ac\geq 0$
• D. $c(a - b + c) < 0$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Show that $\displaystyle \int_{0}^{1}\frac{1}{\left ( 1+x^{2} \right )^{3/2}}dx=\frac{3}{\sqrt{\left ( 2 \right )}}$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
$\displaystyle\int_{0}^{\pi} x\ dx$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Evaluate : $\displaystyle \int _{ -2 }^{ 2 }{ \frac { { x }^{ 2 } }{ 1+{ 5 }^{ x } } dx } .$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Medium
Let $\displaystyle I_{1}=\int_{0}^{1}(1-x^{2})^{1/3} dx$  &  $\displaystyle I_{2}=\int_{0}^{1}(1-x^{3})^{1/2} dx$

On the basis of above information, answer the following questions:

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020