Evaluate. (Be sure to check by differentiating!) 2 1 2 + 7x dx, x* - 7...
Evaluate. (Be sure to check by differentiating! Sote dx, x2 – 3 (Type an exact answer. Use parentheses to clearly denote the argument of each function.)
Evaluate the following integral using trigonometric substitution. 7x² dx (121 + x2) 7x² dx s (121 +x?)? (Type an exact answer.)
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
Evaluate the integral sec 2(7x-2) dx Determine a change of variables from x to u. Choose the correct choice below. O A. u= sec (7x - 2) tan (7x - 2) O B. u=tan (7x-2) O c. u= sec (7x - 2) OD. u = 7x-2 Write the integral in terms of u. sec?(7x+2) dx = S du Evaluate the integral sec2(7x-2) dx = 0
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)
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Find the intervals of convergence of Rx), 7x), Px), and x) dx (Be sure to include a check for convergence at the endpoints of the intervals. Enter your answer using Interval notation.) Σ (a) f(x) X (b) ) X (c) f X (0) Janar
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 using trigonometric substitution. dx S 3 2 (1+x²) dx S 11 2 (Type an exact answer.)
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5. a) Evaluate st -2x + 7x? dx. b) Evaluate: [** sin(x* +1]dx. c) Evaluate: [(3x? –5x+4-4e”)dx
Use the Fundamental Theorem of Calculus to evaluate the following definite integral. 1 2 3 dx 1 2 3 dx √1-x² (Type an exact answer.) S 11