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Calculus, Single Variable: Early Transcendentals (3rd Edition)
- Solution for #3.Set up(and do not evaluate) a (sum of) definite integral(s) equal to the volume of the solid obtained when R is revolved around the line x = −1, using the method of washers.arrow_forwardEvaluate the definite integral. Give the exact answer as a fraction. ∫ 7 ( upper limit ) 0 ( lower limit) ( 2x 2 + x + 6 ) dxarrow_forwardEvaluating integrals Evaluate the following integral. A sketch is helpful. ∫∫R y2 dA; R is bounded by x = 1, y = 2x + 2, and y = -x - 1.arrow_forward
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- Solution for #2:Set up(and do not evaluate) a (sum of) definite integral(s) equal to the length of the graph of y = ln x from the point (1, 0) to the point (e, 1).arrow_forwardEvaluate the integral. Check your answer by differentiating. (Use C for the constant of integration.) (4 −x^5/2)dxarrow_forward3. Evaluate the definite integral. Show your complete solution.arrow_forward
- last follow up to this problem: You can calculate the exact area under the curve using the Fundamental Theorem of Calculus: (in image) where F (x) is an antiderivative of the function f (x) = 4x3. Find an antiderivative of the function f (x). Enter your constant of integration as c. Antiderivative : Now find the exact value of the area under the curve. Area = Notice that your value of c does not matter when you calculate the area under the curve.arrow_forwardApplying reduction formulas Use the reduction formulas in evaluate the following integrals.arrow_forwardEvaluating integrals Evaluate the following integral. A sketch is helpful. ∫∫R 3x2 dA; R is bounded by y = 0, y = 2x + 4, and y = x3.arrow_forward
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