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FRONTLINE COACHING CENTRE, , (NEAR MADRASA ISLAMIA, CLUB ROAD, AURANGABAD (BIHAR)}, CLAss — XII REVISION SET- 08 TIME — 1.30 Hrs., , SUB —- MATH F.M. — 100, , , , , , , , *) Find the value of the following : , , , 1+sin 2x ve, 1) fe x+sin x 2) S xlogx dx, * W fac wave ue onea wea fore fey ey wert oT warHct wie fate (Substitution, method ye er |, cos x 1 (tan “x )* tan~1x y?, 3) ii Jum 4) Jy T4x2 dx, 5 1 xtan x 2 2 z,, 5) Evaluate - fj —— dx 6) Evaluate : Si. sin?x dx, , *anred ot dr & wo 4 freafeftaa ward & AM sa WY], [Evaluate the following integrals as the limits of sums.], 7) f, (x? +1) dx 8) J e* dx, 9) vera agaist ¥ y’ = 4x, x=1,x = 4 cer XT BFE ST TT GENRE |, [Find the area of region bounded by y’ = 4x, x= 1, x® 4.and»eaxis in the first quadrant.], , Zz, 10) Draw a rough sketch of the graph of the curve 4 —+ te =,1 and evaluate the are of, , the region under the curve and above the x ake, 11) Using integration, find the area of the regioneheldsed between the circles x’ + y° = 4, and (x-2)?+ y?=4., 12) Form the differential equation corresponding to (x - a)” + 2y? = a” by eliminating a., 13) Verify that the function y = a cos.x +b six is a solution of the differential equation, , 2, ay -y=0,, 14) shia the differential eqiiation:\, sec” xtan ydx + sec’ ytan xdy = 0., dy _ 3e2*+3e4*, 15) 7 = oe, * Solve the differential equations : 16) x+ygeay 17) x > = y (log y log x+1)., , 18) 4 2 fey Ma, 19) Solve the differential equation x’ dy + y (x + y) dx = 0, given that y = 1 when x = 1., 20) Find the equation of a curve passing through the point (-2,3), given that the slope, , : 2., of the tangent to the curve at any point (x,y) is a, , Name: