ma2176 a4 Integration and its Applications 1. Let ≤≤+<≤−=21if210if3)(xxxxxf. Find 20,)()(0≤≤=∫xdttfxFx. 2. Evaluate the following integrals: (a) dxxx∫+1(b) dxxx∫+221(c) dxeexx∫++1133. Evaluate the following integrals: (a) dxxx∫−12(b) ()dxxx∫+101021(c) ()1021 xxdx++∫(d) 430sin (2 )cos(2 )xx dxπ∫(e) dxxx∫−21(f) dxx∫tan4. Evaluate the following integrals by integration by parts: (a) ∫−dxxex(b) ∫xdxx2sin2(c) ∫xdxarcsin5. Evaluate the following integrals by partial fractions: (a) 322xdxxx+−∫(b) ∫+13xdx(c) ∫++124xxdx6. Evaluate the following integrals: (a) dxx∫−−2221(b) ∫20)(dxxf, where ≤<−≤≤+=212102)(xxxxxf(c) dxxxpqqp∫+10, where 0,>qp7. Find the area of the region cut from the first quadrant by the curve 212121ayx=+. 8. Find the area enclosed by the curvexyln=, the tangent of this curve at
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