Help please? Integral question below. Don’t really understand the concept of integrals in general. Thanks!

Question

1038 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-08T16:19:58

For #g(y) = int_3^y f(x) dx#, FTC part 1 gives us

#g'(y) = f(y)#

Now we want #g''(y) = f'(y)# where #f(y) = int_0^siny sqrt(1+t^2) dt#

Again, using FTC part 1, this time with the chain rule as well, we get:

#g''(y) = f'(y) = sqrt(1+sin^2y) * d/dy(siny)#

# = sqrt(1+sin^2y) cosy#

At #y=pi/6#, we get

#g''(pi/6) = sqrt(1+sin^2(pi/6)) cos(pi/6)#

# = sqrt(1+1/4) (sqrt3/2) = sqrt15/4#