(1) Evaluate

(2) Evaluate

(3) For , prove that

(4) If is a bounded non-negative function, then show that

(5) Evaluate

(6) Evaluate

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(1) Evaluate

(2) Evaluate

(3) For , prove that

(4) If is a bounded non-negative function, then show that

(5) Evaluate

(6) Evaluate

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(1) solution

(2) solution

integration by part here let and

we obtain,

here sub

apply the trig identity

(3) solution

let

since

(4) solution

Let , then we have

Since is odd

(5) solution

integration by parts,

let

then

let

(6) solution

Q.1 的做法太神了…係由答案做返轉頭 定係你睇到d咩令你知道要金做…而且話時話 Q.3 所let的sinh x 係咩?? 都係sin,cos之類的野??

for Q1. because of the power rule. its more of experience

sinh is hyperbolic sine. By definition

you can figure out the rest

sor~ 我想問多個問題~ why我們需要有sinh,cosh這些野的出現??

應該金講~ why我們會去研究佢呢?

We use sin and cos to parametrize circle and ellipses. For hyperbola, we have sinh and cosh.

For details, you can read http://en.wikipedia.org/wiki/Hyperbolic_function