jusr d and e 4. Evaluate the following integrals by making appropriate substitution. fe*(e* 1)?dx + a. esc2x dx cot3...
Using trigonometric identities and substitution, evaluate the following integrals: 1. S sin5 x dx 2. Shamrzdx 3. S V4 – 9x2dx 4. Sýsin? x dx 5. S 1 dx x2 +81
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...
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
3. (A) (Change of Variables) Evaluate the following integrals by making appropriate change of variables. (a) // sin(x2 + y2) dA, where R is the region in the first quadrant bounded by the circle x2 + y2 = 5. YdA, where R is the parallelogram enclosed by the four lines 3. -Y x - 2y = 0, 2 - 2y = 4, 3.x - y = 1, and 3.c - y = 8. zevky / dA, where R is the...
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))...
Evaluate the folloMing integrals. Sec (x) d fe I+E dt Evaluate the folloMing integrals. Sec (x) d fe I+E dt
Evaluate the following integrals Evaluate the following integrals: 3 1 32/2 7 (i) dx 6°2712 dx x²x² + 4 (4x² +9312
Evaluate the following integrals. S 5x-2 dx x2-4 s 9x+25 (x+3)2 dx 2 x3+3x2-4x-12 dx x2+x-6
Problem 2. Evaluate each of the following integrals. a) In(4x) dx 1 4x+1 dx ex b) Jo c) S (5x-2)e 6x dx
Evaluate the following integrals. (a) / In(3x) dx for x > 0 (e) / ( +er) dx (n lete* dx (e) sin(5x +1) dx