Log and Interval Trig Intervals Question 1: Calculate 1 1672 a 1 dx 16 + x2...
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...
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. a) Substitute u = sin(x) to evaluate sin^2(x) cos^3(x) dx. [trig identity sin2(x)+cos2(x) = 1]. b) Find the antiderivatives: i) sin(2x) dx ii) (cos(4x)+3x^2) dx
Calculate the upper sums Unand lower sums Ln, on a regular partition of the intervals, for the following integrals. Note that H represents the Heaviside function as usual: ∫51(7−8x)dx (a) Upper sum Un __________ (b) Lower sum Ln __________ ∫10(4+12x2)dx (c) Upper sum Un __________ (d) Lower sum Ln __________ ∫21H(x−2)dx (e) Upper sum Un __________ (f) Lower sum Ln __________
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...
Calculate the upper sums Unand lower sums Ln, on a regular partition of the intervals, for the following integrals. Note that H represents the Heaviside function as usual: ∫51(7−8x)dx (a) Upper sum Un __________ (b) Lower sum Ln __________ ∫10(4+12x2)dx (c) Upper sum Un __________ (d) Lower sum Ln __________ ∫21H(x−2)dx (e) Upper sum Un __________ (f) Lower sum Ln __________ ∫21f(x)dx where f(x)={10 if x is rational if x is irrational (g) Upper sum Un __________ (h) Lower sum...
Solve the following equations. 1. ln(x2 ) = ln(2x + 3) 2. log2(2) + log2(3x − 5) = 3. 3. Expand the logarithm: log ( x15y13) z19
a) Verify the Rolle's theorem for the function f(x) = -1 x +x-6 over the interval (-3, 2] 3-X b) Find the absolute maximum and minimum values of function f(x)= (1+x?)Ě over the interval [-1,1] c) Find the following for the function f(x) = 2x – 3x – 12x +8 i) Intervals where f(x) is increasing and decreasing. ii) Local minimum and local maximum of f(x) iii) Intervals where f(x) is concave up and concave down. iv) Inflection point(s). v)...
(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.)
14. (a) وع (log x)2 dx = 1°/8. Use the contour, 1 + x2 - 8 -R 8 R Figure 13