1. Find [(x + 7)(x - 5)dx. Hint: Multiply out first. 2. Find (80e58dx 3. Find...
Evaluate the integral. 4) S -2x cos 7x dx Integrate the function. dx (x2+36) 3/2 5) S; 5) Express the integrand as a sum of partial fractions and evaluate the integral. 7x - 10 6) S -dx x² . 44 - 12 6)
arcsin x dx Hint: Use integration by parts. 2. Find the arc length of the portion of the parabola y = 10x - x that is above the x-axis. Find the volume of the solid of revolution if the region between the curves 3. 4. y = x and y = 4x is rotated about the x-axis. Find the area under the curve defined by the experimental data below by using Simpson's rule. MAT2691/101/3/2019 5. Simplify 3 -2 7 4...
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...
1 (a) Evaluate the integral sz? dx. (32-7) 5 2 7 (b)if s f(x)dx = 3 and 5 f(x)dt = 4, find S f(x)dr. 5
Tutorial Exercise Evaluate the integral using the substitution rule. sin(x) 1/3 1* dx cos(x) Step 1 of 4 To integrate using substitution, choose u to be some function in the integrand whose derivative (or some constant multiple of whose derivative) is a factor of the integrand. Rewriting a quotient as a product can help to identify u and its derivative. 70/3 1." sin(x) dx = L" (cos(x) since) dx cos?(X) Notice that do (cos(x)) = and this derivative is a...
dx (x+ 1)(x + 3)(x+ 5)(x + 7) 0
dx (x+ 1)(x + 3)(x+ 5)(x + 7) 0
Evaluate. (Be sure to check by differentiating!) 2 1 2 + 7x dx, x* - 7 122dx 5272 dx= 2 + 7x (Type an exact answer. Use parentheses to clearly denote the argument of each function.
solving step by step
Find the following indefinite integrals: x+1 dx (a) S *7+7x (b) S(Vx? – 5) dx
(1 point) Let [ f(x) dx = 10, f(x) dx = 7, flade = 5. Find f(x) dx = -2 and / * 1054 L. *105(z) – 7 da
Saving... < Question 2 of 5 > Percy tried to multiply 12 (), and his work is shown, but his product is incorrect. Step 1: (*) Step 2: 5x(x-3) 7(5x-3) 5x2-3 35x-21 Step 3: Part A: At which step did Percy make his first error? Part B: What was his first error? Part C: What is the correct product? Select one answer each for Part A, Part B, and Part C.