
evaluate
2 (a) (x2 + 1)2 dx
5. a. By completing the sequence, show that 2 TC dx x2 - x + 1 = 3V3 Hint: d arctan x = dx 1 x2 + 1 b. Show that 3V3 T = (-1)" on
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
(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.)
со tan-1 x dx (х4 + x2 + 1)3 о
со tan-1 x dx (х4 + x2 + 1)3 о
2. (5 pts) Use integration by parts to show that 1- x2 Write x2-x2-1+1 in the second integral and deduce the formula Now, use a trigonometric substitution to conclude that Evaluate 1- x2 dx by using the FTC and then verify your answer by interpreting the integral as the area of a familar shape.
2. (5 pts) Use integration by parts to show that 1- x2 Write x2-x2-1+1 in the second integral and deduce the formula Now, use a trigonometric...
Question 2 please
1 and 2, determine whether or not the integral is In exercises improper. If it is improper, explain why 12. (a) 12 x-2/5 dx 「x-2/5 dx 「x2/5 dx (b) (c) I. (a) 0 13. (a 40 1 dx 2 x 14. (a In exercises 3-18, determine whether the integral converges or diverges. Find the value of the integral if it converges. 15. (a (b)人1x-4/3 dr 3, (a) l.lyMdx (b) x43 dx 16. (a 4. (a) 45 dx...
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
Use a contour to evaluate x? dx (x2 +1)(x2+4) f
Evaluate the following integral using trigonometric substitution. dx s 3 2 (529 + x2) dx 3 2 (529 +x2) (Type an exact answer.)