Let f x -1-2 a 0- i -1 n a i cos ix - j -1 n b j sin j x - then - f x coskxdx then is equal toA- a kB- bkC- - a kD- - bk

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Second Fundamental Theorem of Calculus

Let f x =1/2 ...

Question

Let $f (x) = \frac{1}{2} a_{0} + \sum_{i - 1}^{n} a_{i} c o s (i x) + \sum_{j - 1}^{n} b_{j} s i n (j x), t h e n \int_{- π}^{π} f (x) c o s k x d x$ then is equal to

a_{k}

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b_{k}

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π a_{k}

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π b_{k}

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f (x) = \frac{1}{2} a_{0} + \sum_{i - 1}^{n} a_{i} c o s (i x) + \sum_{j - 1}^{n} b_{j} s i n (j x), t h e n \int_{- π}^{π} f (x) c o s k x d x

For $x > 0$ , let $f (x) = \int_{1}^{x} \frac{log t}{1 + t} d t$ . Then $f (x) + f (\frac{1}{x})$ is equal to

f (x) = |\begin{matrix} \cos x & x & 1 \\ 2 \sin x & x & 2 x \\ \sin x & x & x \end{matrix}|

\lim_{x \to 0} \frac{f (x)}{x^{2}}

f (x) = x^{3} - \frac{1}{x^{3}},

f (x) + f (\frac{1}{x})

\frac{2}{x^{3}}

A = {[a_{i j}]}_{2 \times 2}

a_{i j} = \{\begin{cases} 1 & , if i \neq j \\ 0 & , if i = j \end{cases}

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