Evaluate the integral cos(3x) (1 + 2 sin(3x))\n(1 + 2 sin(3x)) Saint dx
TUI Evaluate the integral. */2 si 63 sin excos 3x dx 0 1/2 S. 63 sin ®x cos xdx=1 0 (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
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 =
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 following integral. 1/2 7 sin ?x -dx 1 + cos x 0 1/2 7 sin 2x dx = V1 + cos x 0 Score: 0 of 1 pt 1 of 10 (0 complete) HW Score: 0%, 0 of 10 pts 8.7.1 A Question Help The integral in this exercise converges. Evaluate the integral without using a table. dx x +49 0 dx X2 +49 (Type an exact answer, using a as needed.) 0
3 cos(3x) I = dx 4+ sin- .1 I= 3cos(3x) -dx 4 + sin²(3x)
5. Evaluate each definite integral. 5.2 dx 2.22 [5] /2 [5] (b) [ COS C sin? C dx 1/4
1. a) Substitute u = sin(x) to evaluate sin^2(x) cos^3(x) dx. [trig identity sin2(x)+cos2(x) = 1]. b) Find the antiderivatives: i) sin(2x) dx ii) (cos(4x)+3x^2) dx
Use the substitution formula to evaluate the integral. 1/2 COS X s dx (5+5 sin x) 0 3 OA 1000 OB 3 200 OC. 3 200 OD. 12 125
Evaluate the following integral. cos 4x dx 11 - sinx S 5л cos 4x dx = S 1 - sin x 51 6 (Type an exact answer.)
Use Green's Theorem to evaluate the line integral sin x cos y dx + xy + cos a sin y) dy where is the boundary of the region lying between the graphs of y = x and y = 22.