Hello,

Could you please solve the following integrals questions and provide explanation.

Thank you!

Find the general antiderivative, F(x), for the given functions. (2) a) f(x) = -sin xcosx b) / (x) = 17-2x 2. Solve the following indefinite integrals, using substitution or integration by parts where needed (3 marks each - 9 marks total) a ) [x(4+x)dx b)JT 1+4x VI+x+2x?"C ) In x 7 2 dx 3. Solve the differential equation =-3cosx-4x? if y() = 0. (2) 4. A stone is thrown vertically upwards, from the edge of a 5 m tall cliff with an initial velocity of 12 m/s. With what velocity does the stone hit the ground? Assume acceleration due to gravity is - 9.8 m/ $2 . Round to the nearest tenth. (3)5. Find the area of the region enclosed by the parabolas y = x and y = 2x-x . Make a sketch and shade in the region of interest. Show all work including finding intersection points. (4) 6. Find the area bounded by the curves y = sin x and y = cosx from x=0 tox = 7 . Make a sketch and shade in the region of interest. Give an exact value answer. (4)