Show detailed work 4. (9 points each) Integration: 77 1 Vx(1+x)2 sinx (b) S3 -dx (6-cos...
TT 4. (9 points each) Integration: (a) Si vachtvasz dx (b) Số 6 cos x) sinx dx 26-2)' ()dx (d) St(t – 5)8dt (e) 56x?=***V7-4 dx
please i need the work with the answers asappp please please TT 4. (9 points each) Integration: dx (a) si veci+V*2 sinx (b) S2 dx (6-cos x)3 (©) 1.6-2) ()dx (d) St(t – 5)8dt 56x?**** 6x7-x*+Vx-4 dx
4. Integration: TT (a) Si Jachtvoz dx (b) sin x dx (6-cos x)3 (c) , (2-2)' (3) dx (d) St(t - 5)8dt 6x7-x*+VX-4 dx x2
Show detailed work 5. (8 points each) Find the limits: V3x2-6 (a) lim X--00 2x -9x (b) lim X-0.x2-sinx COS X (c) lim -X
Evaluate the integral. (Use C for the constant of integration.) (4² + 5x) cos(x) dx Show My Work (Required)
5. (24 points) Evaluate each of the following. Show your work. (e) $1,1x) dx (f) sin(1+1) e* cos(1 – e*) dx (€) Set (ing) dt (h) 1,2 cos(x) cos(sin(x)) dx
ENG 1005 ASSIGNMENTI QUESTIONS (1) Use integration by parts to calculate sin(In(x) dx and Here, In is the natural logarithm. cos(In(x))dx. [5 marks (2) (a) Use integration by parts on sinh(t) sinh(t)dt and the identity cosh (1) = 1+sinh'in to calculate the integral of sinh(r). (b) Calculate the integral of sinh(r) by expanding the product and then integrating, Confirm that you get the same answer as in part (a). (e) Show that if x is a positive real number, then...
show work 9. tan 37 10. sec 4 11. Find sin(x + y) and cos(x + y) if cosx = - cosy = -— x is in quadrant II and y is in quadrant III. [10] 12. Find the exact value of sin 2x and cos 2x if sin x = and cos x = - [6] 5 13. Simplify tan (x + 3) to a form involving sinx, cosx, and/or tanx. [6]
Show that the following integral has the solution, using contour integration in the complex plane: 2.π dx 9-V 3 Determine a fitting path of integration Hint: Show that the sum of the residue/residues of the singular point/points of the 2.T-1 integrand is and use (if appropriate) finally that sin3 -2 to calculate the integral. Show that the following integral has the solution, using contour integration in the complex plane: 2.π dx 9-V 3 Determine a fitting path of integration Hint:...
√9-x² 5. (10pts) Find dx 2 6. (10pts) Show all work for how to compute: ſin(x)dx. (Show work for how to find the antiderivative of In(x), do not just state this antiderivative.) 1