Math+19B+-+Review+1+-+Fall+16 - Math 19B Review 1 Fall 16 1...

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Math 19B - Review 1 - Fall 161.)Express the given integral as the limit of a sequence of Riemann Sums.Thenevaluate the integral by evaluating this limit.(a.)Z21(x2+x)dx(b.)Z2-1(x3-x2+ 1)dx2.) Letg(x) =Zx53sin(t2)dt. Findg0(x).3.) Evaluate limx01xZx0e3tdt.4.) Evaluate.(a.)Z21(3x2-6x+ 1)dx(h.)Zsec5(s) tan(s)ds(b.)Zt2sin(t3)dt(i.)Z10x21 +x6dx(c.)Zcos(y)ydy(j.)Ze4x1 +exdx(d.)Z21e1uu2du(k.)Zsin7(x)dx(e.)Zt5t2+ 2dt(l.)Z101 +y1 +y2dy(f.)Zsin3(φ) cos(φ)(m.)Zπ30sec2(x) tan3(x)3p1 + sec2(x)dx(g.)Ztan2(θ) sec2(θ)(n.)Z2-1x4+x2dx
5.) Find the area of the region bounded by the given curves.(a.)y=x2,y= 2x-x2(b.)y2-x= 1,x-2y= 2(c.)y=x2-9,y= 3-x4(d.)x-2y+y2= 0,y2-4y-x= 0(e.)y= cos(x),y= sin(2x),x= 0,x=π/26.) LetRbe the region bounded byy=x-x2and thex-axis. Find the slope of theline through the origin that divides

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