Question 5. Find the following indefinite integrals: 1. fre'de 4. .Js 3.f x In x dx...
10. (26pts) Find each of the definite integrals, indefinite integrals, and derivatives. 2 dx .22 5) / see?zda (7 - cos x) dc (d) dc sin (x2 – 4) dt (e) ["47" (3+z")" dx () /22"/+ 2 du
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...
Integration by substitution 1. Find each of the following indefinite integrals using integration by substitution: dz (a) / (xºcos(x4) ) do (c) / (sin(2) cromka) die (e) / (24) do (a) / (2.eller) die (0) / (zlog.cz) Integration by parts 2. Find each of the following indefinite integrals using integration by parts: (a) / (+cos(x)) dx (c) / (vVy + 1) dy (e) / (sin”(w) ) at (8) / (sin(o) cos(0) ) da (b) / (x2=+) di (a) / (x2108_(2))...
1 of 4 he following integrals: .nx dx (parts) 4 2) [4x² In(6x) dx parts) 3) 1x*sin2x dx (parts) 4) ſcosº x dx (trig identity) 5) ſsinº x cos*x dx (trig identity) 6) ſcosº xvsin x dx (reduction) 7) ſcot* x dx reduction) 8) ſtan x secºx dx (reduction)
Indefinite integrals. Use table 5.6 or a change of variables to evaluate the following indefinite integrals. check your work by differentiating. 2. 1 dx, x 2 32 xV4x2-I Table 5.6 General Integration Formulas cos ax C a sin ax C 1. cos ax dx = 2. sin ax dr se' 3. 4. ax dx=- ax dx -tan ax C a cot ax C 1 sec ax tan ax dx=-sec ax C 1 --csc ax C csc ax cot ax 5....
solve please Use symmetry to evaluate the following indefinite integrals 5 7 X - x+x dx 5 X 29. 4 2 5 +x 7 Use symmetry to evaluate the following indefinite integrals 5 7 X - x+x dx 5 X 29. 4 2 5 +x 7
4. Evaluate the definite integrals: A) |_ In xdx 1 xV1+ ln² x I dx cos x sin x a f / Inx di -d
Compute the followingelementaryintegrals.(a)dxxxxx3233/2[ 5 ](b)dxxx222[5](c)dxxsin3/0 Question [15] Compute the following elementary integrals. 3x dx 3e-*-2 ex+1 [5] x3 sec?(x4 + 2) dx [4] (b) S (0) Lix - 1dx [6] Question 2 [20] Evaluate the following indefinite integrals. x2 dx [6] (b) f(x+1) tan-+ x dx [6] 10x (c) S x + 3)(x2 + 4x + 13) dx [8] Question 3 [15] (a) Find the area of the region bounded by the parabola x = y2 – 5 and the...
3. Use the u-substitution method to calculate the following indefinite Integrals a. S(x2 - 4)2x dx u= b. Sx?e**dx u= dur C. Sx sinx? dx U= dus
2. Evaluate the following indefinite integrals: (a) vel V=(x+2) dx ET (b) 3. Evaluate the following definite integrals: (a) cos(x) da (sin(x) +18 (b) COS 4. The graph of y=g(t) is shown below, and consists of semicircles and line segments. y=g() -1 3 6 596 s(t) dt Define the function f(x) by f(x)= Use the graph of y = g(t) and the properties of the definite integral to find: (a) the value of (i) f(3) (ii) f(-1) (iii) 1'(6) (b)...