Calculus Evaluate the Integral Problem. Please help!?

Question

Evaluate the integral of:

dx/(sqrt(1-x^2)) in the interval [0,0.1]

Can someone give me a step by step solution to this problem?

Answer 1

i know the integral is arcsin(x) but i will show it through trig substitution

int(dx/(sqrt(1-x^2)))

take x=sin(y)

dx=cos(y) dy

now substitute

int(cos(y) dy/(sqrt(1-sin^2(y))))

int(cos(y) dy/(sqrt(cos^2(y))))

int(dy)

=y

=arcsin(x)

at zero the answer is zero

at 0.1 the answer in radians in 0.100167rad

Answer 2

=arcsinx from 0 to .1

=arcsin.1-arcsin0

=arcsin1

Answer 3

this is just a basic integration formula. for me it is on the inside cover of my calculus book. no work involved, just figure out which integral formula it looks like. this one looks like dx/(sqrt(a^2-x^2)), which equals arc sin of x/a. just plug in the numbers you are given.

the integration will end up as: arcsin x/1, in the intreval [0, 0.1]

plug in 0.1 and zero to get: arcsin 0.1 - arcsin 0.

type it in to your calc to get: 0.1002