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Does this integral Integral(lnxdx) = xlnx + x + C Enter "yes" or "no".

Question : Does this integral Integral(lnxdx) = xlnx + x + C Enter "yes" or "no". : 2163450

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

39) Does this integral ∫(lnxdx) = xlnx + x + C?

Enter "yes" or "no".

40) Does this integral ∫(excosxdx) = (exsinx + excosx/2) + C?

Enter "yes" or "no".

41) Does this integral ∫(3xcosxdx) = 3xsinx + 3cosx + C?

Enter "yes" or "no".

42) Does this integral ∫(sin(lnx)dx) = (xsin(lnx) -xcos(lnx)/2)?

Enter "yes" or "no".

43) Does this integral ∫(xe-x/(x -1)2)dx = (e-x/1 - x) + C?

Enter "yes" or "no".

44) Does this integral ∫(x√(x +3)dx) = (2/3)x(x + 3)3/2 - (4/15)(x + 3)5/2 + C?

Enter "yes" or "no".

45) Does this integral ∫((x2 + x)exdx) = ex(x2 + x - 1) + C?

Enter "yes" or "no"

46) Does this integral ∫(x(x + 2)2/3dx) + (3/40)(2 + x)5/3 (5x - 6) + C?

Enter "yes" or "no".

47) Does this integral ∫(xlnxdx) = (x2/2)lnx - (x2/4) + C?

Enter "yes" or "no".

48) Does this integral ∫(xcosxdx) = xsinx + cosx + C?

Enter "yes" or "no".

49) Does this integral ∫(sinxsec2xdx) = sinxtanx + cosx + C?

Enter "yes" or "no".

50) Does this integral ∫((x + 2)sin2xdx) = (1/4)sin2x - ((x + 2)/2)cos2x?

Enter "yes" or "no".

51) Does this integral ∫(ln(lnx)/x)dx = lnx(ln(lnx) -1) + C?

Enter "yes" or "no".

52) Does this integral ∫(x + 1/e2x)dx = (-e2x/4)(2x + 3) + C?

Enter "yes" or "no".

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

53) Which of the following accurately describes integration by parts?

A) ∫(f(x)g'(x)dx = f'(x)g(x) - ∫(f'(x)g(x)dx)

B) ∫(f(x)g'(x)dx = f(x)g(x) - ∫(f'(x)g(x)dx)

C) ∫(f(x)g(x)dx = f'(x)g'(x) - ∫(f'(x)g'(x)dx)

D) ∫(f(x)g(x)dx = f'(x)g(x) - ∫(f(x)g'(x)dx)

E) none of these

54) Decide whether integration by parts or substitution should be used to compute the indefinite integral

∫(ln4xdx)

If substitution, indicate the value of u; if by parts, indicate f(x) and g(x).

A) integration by parts; f(x) = ln4x, g(x) =1

B) integration by parts; f(x) = 1, g(x) = ln4x

C) integration by parts; f(x) = lnx, g(x) = 4x

D) substitution; u = 4x

E) none of these

55) Decide whether integration by parts or substitution should be used to compute the indefinite integral

∫(cos(lnx)/x)dx

If substitution, indicate the value of u; if by parts, indicate f(x) and g(x).

A) substitution; u = lnx

B) substitution; u = (lnx/x)

C) integration by parts; f(x) = 1, g(x) = (cos(lnx)/x)

D) integration by parts; f(x) = cos(lnx), g(x) = (1/x)

E) none of these

56) Decide whether integration by parts or substitution should be used to compute the indefinite integral

∫(-e1/x/x2)dx

If substitution, indicate the value of u; if by parts, indicate f(x) and g(x).

A) substitution; u = (1/x)

B) substitution; u = x-2

C) integration by parts; f(x) = -e1/x, g(x) = (1/x2)

D) integration by parts; f(x) =- (1/x2), g(x) = e1/x

E) none of these

Solution
5 (1 Ratings )

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