8.)Evaluate: a.) S 4x® dx. b.) ſ 4x2Vx3 + 3 dx. c.) S(x3 +1 )2 dx.
Evaluate 4 cot – 3x csc 4x dx.
What values of a and b maximize the value of ſ(4x-x2) dx? (Hint: Where is the integrand positive?) and b=maximize the given integral. (Simplify your answer. Type a whole number.) a =
Use the Fundamental Theorem to evaluate the definite integral exactly. ſ (18x? +7) dx Enter the exact answer. ſ (18x? + 7) dx =
evaluate and simplify I = S 3x44 3x+4 Xr2xts dx
7 Evaluate the integral ſ (lx) – V49 – x2) dx by -7 interpreting it in terms of areas. Show your work in the PDF version of the test.
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
Evaluate the integral using the given substitution. ſ Vacos (x32-7) dx, u = x 3/2_, o x312 sin 2(x3/2 - 7)+ C o sinᵒ (8312.7) + C a o 1/3 (4x) sin (x3/2 -7)+C o $(x3/2 - 7) + sin 2(x3/2 - 7) + C
23 dx 31. J x ſ(4e' + 3x)dx s(ue' 32. jczVelde 33. 34. Find the area under the graph of y=-x*+8x over the interval [0, 2] 35. Use the properties of logarithms to simplify log, 45 ir log, 3 -.7925 and
Evaluate the integrals. 3x2 - 4x+7 dx (x2–2)2