# The curve with equation #y = h(x)# passes through the point #(4, 19)#. Given that #h'(x) = 15xsqrtx-40/sqrtx#, find #h(x)#?

##### 1 Answer

Mar 4, 2018

since

the antiderivative or indefinite integral of

therefore

this can be integrated easily by using the inverse of the Power rule

and it comes out as

to find C, we can use the fact that

so

therefore

therefore, the entire function

#h(x) = 6x^(5/2) - 80x^(1/2) - 13#

and you can factorise it more if you want