Question

Question 2 (Learning Outcome 2) 0 S (*x+3) dx S A) Evaluate the following integrals. 4x+7 2x+5) 5x2–2x+3 (ii) dx (x2+1)(x-1) x2+x+2 (iii) S3x3 –x2+3x+1 dx dx (x+1)V-x-2x In (x) dx (iv) S x2 X+1 (vi) S dx (1+x2) (vii) S dx x(x+Inx) (viii) Stancos x) dx (ix) 30 Sin3 e*(1 + e*)1/2 dx dx 2 sin x cos x (x) S B) Find the length of an arc of the curve y =*+ *from x = 1 to x = 2. C) Determine the area bounded by the curves y = Vx and y = x -2. D) Find the volume of solid generated by revolving the curve y = V around the line x = 6 and the region bounded by y = 0 and x = 4. E) Estimate the integral 52 dx numerically with 4 equal interval partitions and estimate the error by: (i) Simpson's rule (ii) Trapezoidal rule Repeat the above by using & equal interval partitions and elaborate the improvement in accuracy with higher interval partitions.

Answer 1

rib I= flux + 7) de 22C+5 32 June +10 - 3dra 2x +5 2127+-) -2 24+5 [स dx - 3 fle dac op te fiador 3 •JAP 2x+5 T N 312 (220 + 5) +c 2x .

%3D (M 1522 2x +2) dr Ex-1) 224) ((२४ 2 2x + 3x + 3 Jdx ___20 -1) (x241) [२rcr-1) +3/x2+12 (x-1) x+D + 3. 2 22241 Jodic (1-X) 2x dx dac 1 12+1 24-1 । let x²+1=4 2x doc=dt + ४ dx 1 + 24-1 Jn(1) + 3100-1) + C J - 10/x241) + 3 Jap-1) +C

- I ابنها رود-لری let در جا الم ہی أولى - 220-2 - - 21 doc 2 x 1²2x du - 22 dx 2q dy کر لو ۔ put this value to o الى - ! كالعے عهود ) - دردد fixed fa dy الر- 22 2عد - 1. dy L ( دلیل four Idy .(+U/ي Hlutus tdy سلما ز-u) لا- ام صلاء 1 + في+الصلا

I In Lx²gx-1 t6 المرور A N for دو عامل 2 Let Inxht = L dir=dt C = ft t dt f tedt et et tot f integsegte by parts #fētdi -Slot Voldt I

- tett L ق ) دلم * ) = لام . *م - . (در صر putt (3/ Jr ۔ Inix) E : - 10/3) e e + C - نصر - T C+ اتری علاء ( ولا 2
according to me question A(iii) is not correct