Applications of Integration

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1. 1. Evaluate the integral (leave your answer in exact form): TT / 4 3 sin(2. ) esin(x) dx 7 / 6 2. 2. Evaluate the integral: In(esec? (7x) ) dx3. In Exercises find the average value of the function over the indicated interval. Find a point in this interval at which the function takes on the average value. f(x)=6x2, xE [0,2 ]4. 4. The Gateway Arch in St. Louis is 630ft high and has a 630-ft base. Its shape can be modeled by the parabola 630 [1 - (315) ] Find the average height of the arch above the ground. YA y = 630 (1 - 315 500- 400- 300 630 ft 200- -630 ft 100- -300 -200 -100 0 100 200 3005. 5. Use the open space to show all of your work. This includes: sketching the curves, finding and labeling the points of intersection, setting up the appropriate definite integral(s) and evaluating them. Place your numerical answer for the area of the region in the box. Leave your answer in exact form. Sketch the region bounded by the curves and find the area of that region. y= x, y= 5x-x3 6. 6. Find the area between the 2 curves by integrating with respect to y. Use the open space to show all of your work. This includes: sketching the curves, finding and labeling the points of intersection, setting up the appropriate definite integral(s) and evaluating them. Place your numerical answer for the area of the region in the box. Leave your answer in exact form. Sketch the region bounded by the curves and find the area of that region. x=y', x - 3y =2