(a)Prove that∫2a0f(x)dx=2∫a0f(X)dx,if f(2a−x)=f(x) and evaluate

1.	(a)Prove that∫2a0f(x)dx=2∫a0f(X)dx,if f(2a−x)=f(x) and evaluate∫2π0cos5xdx if f(2a−x)=−f(x) (b) Find the values of a and b such that the function defined by f(x)=⎧⎪⎨⎪⎩5,if x≤2ax+bif 2<x<10 is a continous function21,if x≥10
Answer» $(a) P r o v e t h a t \int_{0}^{2 a} f (x) d x = 2 \int_{0}^{a} f (X) d x, i f f (2 a - x) = f (x) a n d e v a l u a t e \int_{0}^{2 π} c o s^{5} x d x$ $i f f (2 a - x) = - f (x)$ (b) Find the values of a and b such that the function defined by $f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} 5, & i f x \leq 2 a x + b & i f 2 < x < 10 i s a c o n t i n o u s f u n c t i o n 21, & i f x \geq 10 \end{matrix}$

(a)Prove that∫2a0f(x)dx=2∫a0f(X)dx,if f(2a−x)=f(x) and evaluate∫2π0cos5xdx if f(2a−x)=−f(x) (b) Find the values of a and b such that the function defined by f(x)=⎧⎪⎨⎪⎩5,if x≤2ax+bif 2<x<10 is a continous function21,if x≥10

Answer»

$(a) P r o v e t h a t \int_{0}^{2 a} f (x) d x = 2 \int_{0}^{a} f (X) d x, i f f (2 a - x) = f (x) a n d e v a l u a t e \int_{0}^{2 π} c o s^{5} x d x$
$i f f (2 a - x) = - f (x)$

(b) Find the values of a and b such that the function defined by

$f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} 5, & i f x \leq 2 a x + b & i f 2 < x < 10 i s a c o n t i n o u s f u n c t i o n 21, & i f x \geq 10 \end{matrix}$

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(a)Prove that∫2a0f(x)dx=2∫a0f(X)dx,if f(2a−x)=f(x) and evaluate∫2π0cos5xdx if f(2a−x)=−f(x) (b) Find the values of a and b such that the function defined by f(x)=⎧⎪⎨⎪⎩5,if x≤2ax+bif 2&lt;x&lt;10 is a continous function21,if x≥10

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(a)Prove that∫2a0f(x)dx=2∫a0f(X)dx,if f(2a−x)=f(x) and evaluate∫2π0cos5xdx if f(2a−x)=−f(x) (b) Find the values of a and b such that the function defined by f(x)=⎧⎪⎨⎪⎩5,if x≤2ax+bif 2<x<10 is a continous function21,if x≥10