wkst-6.pdf - Worksheet 6 The Fundamental Theorem of Calculus Integration by substitution 1 Find the following derivatives Z x d(1 t)200 dt(a dx 1 Z 0

wkst-6.pdf - Worksheet 6 The Fundamental Theorem of...

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Worksheet 6 The Fundamental Theorem of Calculus; Integration by substitution 1. Find the following derivatives:(a)ddxZx1(1 +t)200dt(b)ddxZ0e-xln(t2+ 1)dt2. LetF(x) =Zx21ln(t)dtforx2.(a) FindF0(x).(b) IsFincreasing or decreasing? What can you say about the concavity of its graph?3. Find the following integrals:(a)Zxe-x2dx(b)Zt2(t3-3)10dt(c)Z14-xdx(d)Z(lnz)2zdz(e)Zet+ 1et+tdt(f)Zz(z+ 1)1/3dz(g)Zt2+tt+ 1dt(h)Z3x-22x+ 1dx(i)Z1p1 +xdx.

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