Evaluate the following integral. X2 + 16x-4 S*** dx x2 - 4x Find the partial fraction decomposition of the integrand. 1 * +18 x2 + 16x-4 dx = x² - 4x JOdx Evaluate the indefinite integral. *x? + 16x-4 dx = 3 х - 4x
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
s više dx V16 – x2 -√16 – x² x' +C V16 – x2 2x +C V16 - x² + c 16 - x2 2x +C 1 point 5 x2 dx = x3 +4 In | x3 + 4[ + C In [x] + + +C O In | x3 +41 whe in* +4 +C + 4x|+C
(1 point) Find a particular solution to dy dy x2 + 4x + 2y =x' sin(x). dx in x > 0 ур
(1 point) Find a particular solution to dy dy x2 + 4x + 2y =x' sin(x). dx in x > 0 ур
1.) Find the definite integrals a.) sdx b.) S dx x2-4x+9 c.) ſ 4arccos xdx d.) Se-3x sin 5xdx e.) S In(4 + x2)dx f.) s cosst dt sin t g.) St tan 5 2xsec 4 2xdx h.) ſ sin(-4x)cos3xdx
2. a) Find an approximation to the integral (%(x2 - 4x) dx using a Riemann sum with right endpoints and n=4. b-a and x,-a +Ax. Use this to b) Using the definition ()dx = lim Žf(x7)Ar, where Ar = ? evaluate 1, (x2 - 4x) dx
Evaluate the following: csc(x) cot(x) dx i) s 2-csc (x) ii) S x sin(4x) iii) 6. x sin(x2) dx iv) x x + 3y = 3
(2) Calculate the following integrals: х 2.x3 – 4x + 3 -dx (x + 1)2(x2 +1) Java 2 - 25 2 dx x4V x2 – 25 (3) Explain why, using the techniques we've learned so far, we are able to calculate the integral of any rational function. (A rational function is one of the form p(x) where g(x2) p and q are polynomials.)
13. S(3 – 2x – 4x²)(1+4x) dx 14. S Inx) dx =
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...