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- Change the function y=3(0.5)x to one having e as the base.arrow_forwardShow detailed solution for the following definite integral: (Non-anonymous questionO) 2+w4 dw w³+9warrow_forward2. Find the following definite and indefinite integrals. O Parts a, b, and c: For the indefinite integrals, you do not need to simplify your final O a. answer. Parts d and e: For the definite integrals, simplify your answer and write your answer in exact form. Do not use a calculator. [(x-3 + 5x5/2+√3)dx [(-e² +13) dx d. e. (²2-√x) dx (ex - x)dx L² (2x - J-3 (2x - 1)dx Oarrow_forward
- find an antiderivative for each function. Do as manyas you can mentally. Check your answers by differentiation. √x + 1/√xarrow_forwardpls. evaluate the following and provide correct answer and solution. Thank You.arrow_forward3. Jay is doing his mathematics homework on the run. He managed to squeeze in one problem between lunch and his expository writing class. He used his calculator to find Ln, Rn, Tn, and M₁, to approx- imate a definite integral and jotted down the results on a napkin. The values of Ln, Rn, Tn, and M₁ were: 0.367617, 0.3211885, 0.341189, and 0.274760. He didn't write down the problem, nor did he record the value of na he used. But he did sketch the function (over the relevant interval) on the napkin; it looked like this. He wants your help in labeling the data he recorded as a left-hand sum, a right-hand sum, a midpoint sum, and a trapezoidal sum. Which is which? Explain your answer in complete English sentences.arrow_forward
- Complete the following problems related to Definite Integrals and F.T.O.C II Homework Problems: Use geometry to evaluate the following definite integrals. Sketch a graph of the function, show the region in question, and interpret your result. 1. (8 – 2x) dx 2. ²₂(2x + 4) dx 3. √16 - x² dxarrow_forwardA student wants to complete a problem for extra credit. The work for the definite integral is shown in the process below. Review the work of the student and determine whether the student has earned extra credit for the problem. If not, then explain where the student needs to correct any work or improve the work shown. Then find the correct value of the definite integral by showing the correct evidentiary work. If it is determined the student’s work is correct, then explain where the student can improve their work.arrow_forwardcalculated, and dr 1000 1 dx. 1 x²arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage