Find the following integrals, showing all working. (a) [2x² (x³ + 5)³/² dx (b) / (c) 4 (d) [* 5x x²-1 dx (4e-2 + t³) dt e3√√-2 2√√√ dx

Calculate the main value for ln(−3 + 3√3j)

S ((V80 – x² ) – (0.3cos(1.2r + 1.3) + 5) )ar

(A) a B) b (D) d ²1dx = √( + g(x)) dx, then A + √² g(x) dx is equal to A. -1 B. -1 + In(5/2) C. 1 D. -1 + In(7)

Find the error in the following work:

Three definite integrals are listed below. Two can be evaluated exactly using geometry. One cannot. The integrals: -3 L Iv9 (a) Write one of the integrals that can be evaluated using geometry, and then evaluate it. [2x+3dr 2x + 3 dx √9 - x² dx √9 - x² dx (b) Write the other integral that can be evaluated using geometry, and then evaluate it. (c) Briefly explain why the third integral cannot be evaluated using geometry.

2. Find the quotient and remainder of the following functions by long division. Write the answers in the form P(x)=Q(x)·D(x)+R(x). -4x' +2x -x+1 2x' – 7x² + 7x + 15 b) x+2 x² -3

2sin(2x)=√3

Part A: Multiply (5x2 + x − 4)(x + 2). Part B: Multiply −3x2(6x2 + 2x − 3). Part C: Let f(x) = x2 + 3x − 4 and g(x) = x + 5. Find f(x) ⋅ g(x). Part D:  Which of the following represents the area of a rectangle whose length is 5x − 3 and whose width is x + 7?  5x2 − 21  5x2 + 9x − 21  5x2 + 32x − 21  5x2 − 32x − 21

2.(8) Make sure to simplify your answer using positive fractional exponents.