Integration (CIE A Level Maths: Pure 1)

Use calculus to find

Evaluate

Find the equation of the curve passing through the point (4, 64) and given by

Show that

Hence, or otherwise, work out

Given

find the value of the positive constant 

Given  and that when ,,  show that

Find an equation for y in terms of x, given that when , .

Use calculus to show that

where  is a constant.

By first considering the limit of as ,  determine the value of

Use calculus to find the value of

Find the equation of the curve passing through the point (-2, 3) and given by

Using the binomial expansion, or otherwise, show that

Hence, or otherwise, work out

Given

find the value of the constant p, where .

A function,, has second derivative given by

Given that , and find

Use calculus to find the exact value of each of the following improper integrals:

Use calculus to find

Use calculus to find the value of

giving your answer correct to 3 significant figures.

Find the equation of the curve passing through the point (4, -8) and given by

Show that

Hence, or otherwise, work out

Given

find the value of the constant q.

A function, , has second derivative given by

Given that and are factors of , find .

Given that

where  is a real constant, find the value of .

Given that

where  is a real constant, find the value of .