Please show complete solution/explanation Subject: Integral Calculus

III. PROGRESS CHECK: Find the area beneath a curve and evaluate integrals. Draw the figure, sketch the curve and boundary lines. 1. Find the area under the curve y = 2x - x from x = 1 to x = 2 with n = 4 inscribed rectangles. 2. Find the area under the curve y = 2x - x from x = 1 to x = 2 with n = 4 circumscribed rectangles. 3. Find the area under the curve y = 2x - x from x = 1 to x = 2 with n = 4 using the Trapezoid Rule. 4. Find the area under the curve y = 2x - x from x = 1 to x = 2 with n = 4 using Midpoint Formula. 5. Find the area under the curve y = 2x - x- from x = 1 to x = 2. 6. Evaluate J_cos x dx 7. Evaluate J, 2x Vx dx 8. Evaluate Jo (x* - 5x3 + 3x2 - 4x - 6)dx 9. Evaluate [ Ixldx 10. Evaluate sin x dx