Evaluate the definite integrals using the graph of f(x) below. y 4 2- O -2- 2 A T T I 1 I 1 -00 8 10 I 1 I I I I 1 1 12

d 3 Evaluate dx √√In(6 - x²) at x = 1.

Find the indefinite integral and check the result by differentiation.

√√2/2 11x² Jo 11 arcsin(2v/2 2 dx V1-x² 11 sin(2arcsin(2V/2)) 4 X

Evaluate the definite integral. (Be sure to show your work.) (a) / (2³ + 1)dx (sin x + 1)dx 2 (b) / 3 7) dx x2 (d) / (x³ + 7x)dx (23

Express the rational function as a sum or difference of two simpler rational expressions. ess 3x2 3x2 (x-1)(x + x + 1) 193. x' - 1

Consider the function f(x) = 6x + 12 sin x on the domain [0, 2π]. Use analytic techniques (calculus, algebra, trigonometry) to determine the intervals where the function is increasing and decreasing. Use exact values in your response. f(x) is increasing on f(x) is decreasing on

Find the indefinite integral and check the result by differentiation.

Evaluate the definite integral

Find the indefinite integral for the function using the substitution u - X √s 8x² + 7. -dx + 7 S X -dx √ex 8x +7