hw1_sp19.pdf - Math 115 Assignment 1 1 Evaluate Z y3 2...

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Math 115 Assignment 1
8. Use the substitutionu=π-xto show thatintegraldisplayπ0xf(sinx)dx=π2integraldisplayπ0f(sinx)dx.For each of the following area questions, sketch the region and draw a typical approximating rec-tangle.9. Find the area of the region between the curvesy= 8-x2andy=x2(but not bounded bythex-axis) on [-3,3] .10. Find the area of the region bounded by 4x+y2= 12 andx=y.11. Find the area of the region between the curvesy= sinxandy= sin 2xon [0, π/2] (but notbounded by the

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