Concept explainers
Choosing an Antiderivative In Exercises 3 and 4, select the correct antiderivative.
(a)
(c)
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Calculus (MindTap Course List)
- Different methods x2 -dx using the substitution u = x + 1. x + 1 a. Evaluate b. Evaluate - - dx after first performing long division x + 1 on the integrand. c. Reconcile the results in parts (a) and (b).arrow_forwardUsing integration by parts, [4x22x dx Select one: A. (4x²-4x+1)e2x+C B. (2x2-4x+1)e²x+C C. (4x²-2x+1)e²x+C D. (2x2-2x+1)e2x+Carrow_forwardd (3x2 + 11)e¯ª at x = -1. dx Evaluate d (За2 + 11)е dx = x=-1arrow_forward
- Use the areas shown in the figure to evaluate f (x) dx. Area = 10 Area = 9 а b c d y = f(x) Area = 94 A 113 B - 75 -113 75arrow_forwardUsing substitution: Describe why fr (5 – 22) da + Su'du where u = 5 – a2. %3Darrow_forward√r² - a² (2) Find the integrals: x² √36x² S sv •S x² √36 + x² dx dxarrow_forward
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