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- Write a definite integral that represents the area of the region. (Do not evaluate the integral.) y₁ = x² + 2x + 5 = 2x + 14 Y₂ = Y ~ 20- 15- 10- dx y2 2 yl X 4arrow_forwardFind the area between y = x - 2 and y = x“ – 4. Round your limits of integration and answer to 2 decimal places. 14+ 12 10- 구 -4 2 -5 -4 -3 -2 -2 The area between the curves is square units. Add Work Check Answerarrow_forwardReversing the.orderof integvation 4-2x- dy.dx- (6) o2arrow_forward
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- Evaluate the integral below by interpreting y=f(x) it in terms of areas in the figure. A1 The areas of the labeled regions are АЗ 10 15 A2 A4 A1= 6, A2=4, A3=2 and A4=2 7 10 V = | f(x)dx (figure is NOT to scale) V = 3.arrow_forwardestion dx Using an appropriate substitution, the integral is equal to: x2+6x+14 (Complete the square, if necessary). ( 3)arrow_forwardy=f(x) A1 АЗ 3 15 A4 A2 10 (figure is NOT to scale) Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the labeled regions are Al= 6, A2=3, A3=1 and A4=2 V = |f(x)| dx V = Enter your answer as a whole numberarrow_forward
- Evaluate the integral below by interpreting y=f(x) it in terms of areas in the figure. А1 The areas of the labeled regions are АЗ A1= 7, A2=4, A3=2 and A4=1 3 5 A4 10 A2 (figure is NOT to scale) V = V =arrow_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_forward(у - 3)2 In the graph to the right, the equation of the parabola is x= and the equation of the line is y = 13-x. Find the area of the shaded region. Set up the integral that will give the area of the region. Use increasing limits of integration. Select the correct choice below and fill in any answer boxes to complete your choice. (Type exact answers.) O A. O dy O B. ( ) dx The area of the shaded region is (Type an exact answer.) 7arrow_forward
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