Solve the intergral ?
(i) Use trigonometric substitution to evaluate the intergral:
#int_0^sqrt(2)# #(dx)/((x^2+2)^2#
(ii) Solve the integral equation
#int_1^x# #f(t) dt = f(x) - 5#
where #x>=# #1# and express your answer as an exponential.
(i) Use trigonometric substitution to evaluate the intergral:
(ii) Solve the integral equation
where
1 Answer
First problem:
Guessing that we should try this transform:
This leaves:
The second problem:
Using Liebnitz's Rule:
Which solves as:
With this theme: