Double integrals—your choice of transformation Evaluate the following integrals using a change of variables. Sketch the original and new regions of
31.
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- ament 22 - Integration by Parts K www.aviatormast... Evaluate using integration by parts or substitution. Check by differentiating. (5x²-2x) ex dx [(5x²-2x) e 7x dx =arrow_forwardEvaluate the definite integral.. Use the integration capabilities of a graphing utility to verify your result. 2x Vx+ 16 Step 1 To find the definite integral dx, apply the basic integration rule. V X + 16 Let u = x² + 16. Differentiate u in terms of x, du= x dx.arrow_forwardx dx V 1-x2 find the value ? Specify the integral varieties?arrow_forward
- Evaluate the definite integral. Use the integration capabilities of a graphing utility to verify your result. 2x dx Vx2 + 16 Step 1 2x To find the definite integral Vx + dx, apply the basic integration rule. + 16 Let u = x² + 16. Differentiate u in terms of x, du = A 2 x dx. Step 2 Rewrite the integration in terms of u. 2x x = 3 du V x2 + 16 = xp Step 3 Apply the power rule of integration. rx = 3 x = 3 du = du +1 1x = 3 +1Jo 1x = 3arrow_forwardEvaluate the definite integral. Use the integration capabilities of a graphing utility to verify your result. 2x x² + 16 xp Step 1 2x To find the definite integral Vx² + dx, apply the basic integration rule. Let u = x² + 16. Differentiate u in terms of x, du = 2 x dx. Step 2 Rewrite the integration in terms of u. 2x dx = du x² + 16arrow_forwardConsider the following. y y = x+2 y = x? -3 -2 -1 1 (a) Find the points of intersection of the curves. (х, у) - (smaller x-value) (х, у) %3D (larger x-value) (b) Form the integral that represents the area of the shaded region. dx (c) Find the area of the shaded region. 3.arrow_forward
- SFER BASIC CALCULUS (C TRANSFER TRAN SFER ACTIVITY 2: INTEGRATION THROUGH SUBSTITUTION Direction: Evaluate the following integrals. 2. S dx Vx3+5arrow_forward2e dx 2x +3 Evaluate the integralarrow_forwardEvaluate the definite integral. Use the integration capabilities of a graphing utility to verify your result. 2x dx +16 Step 1 2x To find the definite integral dx, apply the basic integration rule. x² + 16 Let u = x + 16. Differentiate u in terms of x, du = 2 2 x dx. Step 2 Rewrite the integration in terms of u. x 3 1 1 du 2x x +16 Vu Step 3 Apply the power rule of integration. X= 3 x = 3 -1/2 -1/2 du du = -1/2 -1/2 + 17x = 3arrow_forward
- Evaluate the definite integral. Use the integration capabilities of a graphing utility to verify your result. 2x dx x2 + 16 Step 1 2x To find the definite integral dx, apply the basic integration rule. + 16 Let u = x2 + 16. Differentiate u in terms of x, du = 2 2 x dx. Step 2 Rewrite the integration in terms of u. 2x du dx = V x2 + 16arrow_forwardThe integrand of the definite integral is a difference of two functions. 5 - X dx 15 15 Sketch the graph of each function and shade the region whose area is represented by the integral. 6. 4 y y 2- 2 4 6. 4 4 y y 2- 2 8.arrow_forward13 2x To find the definite integral dx, apply the basic integration rule. X + 16 Let u = = x< + 16. Differentiate u in terms of x, du = 2 2 x dx. Step 2 Rewrite the integration in terms of u. 2x x= 3 du x² + 16 Jo Submit Skip (you cannot come back)arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,