3.) a.) Evaluate the following integral. (15 points) in(1 +5x?) dx b.) Evaluate the following integral. (10 points) tanº (6x) sec 10 (6x) dx
14 of 15 (0 complete) Evaluate the definite integral J (1x² - 6x + 5) dx (7x² - 6x + 5) dx = 0 (Simplify your answer.)
EXAMPLE 2 Find sin$(7x) cos”7x) dx. SOLUTION We could convert cos?(7x) to 1 - sin?(7x), but we would be left with an expression in terms of sin(7x) with no extra cos(7x) factor. Instead, we separate a single sine factor and rewrite the remaining sin" (7x) factor in terms of cos(7x): sin'(7x) cos”(7x) = (sinº(7x))2 cos(7x) sin(7x) = (1 - Cos?(7x))2 cos?(7x) sin(7x). in (7x) cos?(7x) and ich is which? Substituting u = cos(7x), we have du = -sin (3x) X...
Evaluate the integral. -3+e-6x dx 5x 33 +C O 30 e-11x33e6x + 5) + C o 1-3*43e64-5)+c O-3e-11x11e5x + 1) +
Use the given transformation to evaluate the integral. -5x dx dy where R is the parallelogram bounded by the linesy-x+1, y-x +4 y#2x+2y»2x + 5 A) -5 B) 10 C)5 D)-10 32) y+ x where R is the trapezoid with vertices at (6,0), ,0).。. 6), (0.9) 45 45 B) ÷ sin l 45 C) sin 2 45 A) sin 2 Use the given transformation to evaluate the integral. -5x dx dy where R is the parallelogram bounded by the linesy-x+1,...
evaluate the integral Evaluate the integral. [ 6x dy dx 0 - 1734 O 1020 0 - 204 O 102
Use substitution to find the indefinite integral. 6x + 7 (12x² + 28x) 5 6x +7 16x +7 (12x² + 28x) 5 dx = 0
Evaluate the integral cos(3x) (1 + 2 sin(3x))\n(1 + 2 sin(3x)) Saint dx
1. Evaluate the indefinite integral sen (2x) – 7 cos(9x) – sec°(3x) dx = 2. Evaluate the indefinite integral | cor(3x) – sec(x) tant(x) + 9 tan(2x) dx = 3. Calculate the indefinite integral using the substitution rule | sec?0 tan*o do =
Evaluate the definite integral. 5 S (5x2 - 6x +6)dx 0