Mathematics

# Let $f(x) = \dfrac{1}{2} a_0 + \sum^n_{i = 1} a_i \, \cos (ix) + \sum_{j = 1}^n \, b_j \, \sin (jx)$. Then $\underset{-\pi}{\overset{\pi}{\int}} f(x) \, \cos \, kx \, dx$ is equal to

$\pi a_k$

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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 Hard
Find:$\displaystyle\int_{-\pi}^{\pi}{\dfrac{{\cos}^{2}{x}\,dx}{1+{a}^{x}}}$ where $a>0$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Simplify:-
$\int {\left( {1 - x} \right)\left( {2 + 2x} \right)dx}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
The value of $\displaystyle \overset{a}{\underset{-\pi}{\int}} \dfrac{\cos^2 x}{1 + a^x} dx, a > 0$ is
• A. $-\pi$
• B. $\dfrac{\pi}{2}$
• C. $2\pi$
• D. $\pi$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
$\int {x{{\sin }^2} x\times dx}$

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