Poly Integration,Pls help

787180 SG

a) Integrate sin(square root x)dx

b)Integrate square root(1+xsqare)dx.

Greatly appreciate for the help

eagle SG

Not sure if u hv learned the methods before... but

a) substitute x = y^2, then integrate by parts using LIATE rule
b) substitute x = tan y, then integrate by splitting sec^3 x to sec x (1 + tan^2 x)

wee_ws SG

Hi,

To expand on what eagle has mentioned, you need to use a suitable substitution.

In (a), let y = sqrt(x). Then dy/dx = 1 / {2sqrt(x)} = 1/2y.

So, integral sin (sqrt(x) dx = integral (sin y) (dx/dy) dy

= integral (sin y) (2y) dy

Next, we use integration by parts. By the LIATE classification, sin y is 'T' and y is 'A'. 'A' comes before 'T', so the rule says that we differentiate sin y and integrate y.

Hope it'll help you to proceed, as these questions are hard without guiding steps given in the problem statement.

Thanks!

Cheers,
Wen Shih