INTEGRAL CALCULUS

Hi. Kindly answer all the questions below, I badly needed it all to be answered. Please make it legible as much as possible, and box your final and correct answer. Thank you very very much.

Part 1. Evaluate the following integrals (I5 pts each}. 13d: {xi +9255 it 2' I2+2x Part 2. Problem soiling. 1. At any' point (x v) on a particular curve the tangent line has a slope equal to 3x2 1. If the curve contains the point (1 8}, nd its equation. {5 pts} 2. Solve the particular solution forx: = 2 41: when points (I) 2] and { l 3) are on the curve. {T pts} 3. The volume of a balloon is increasing according to the formula %= v\": + 1 +- 2,: where Verna is the volume of the balloon at r. seconds. If V- 33 and when t- 3 SEE then nd the volume of the balloon at 8 seconds. (T pts] 4. The rate of net investlnent is given by { 1' = {1 + 4082\"\": + 12.1:1'Ira + t and the initial stock of capital at t- is 31] units. Find the equation for the stock of capital UPS}