A series of integral based questions?
#\intx^5\ln(x)dx#
My answer: #x^6/6(\ln(x)-1/6)+C#
#\int\sec^3(x)\tan(x)dx#
My answer: #1/3\sec^3(x)+C#
#\int(x^3)/(x^2+1)dx#
My answer: #x^2/2-2\ln|x^2+1|+C#
#\int(5x)/(x^2-3x)dx#
My answer: #5\ln|x-3|+C#
- Find the area of the region bounded by
#y=4-x^2# and #y=2x+1# .
My answer: #27/3#
- Find the volume of the region bounded by
#y=x^3# , #y=0# , and #x=3# , revolved around the y-axis.
My answer: #(243\pi)/5#
- Approximate
#\int_2^4\sqrt(x-2)dx# using the Trapezoidal rule, rounding to 4 decimal places.
My answer: #\approx1.8195#
#\int_1^\infty(\tan^-1(x))/(x^2+1)dx#
My answer: divergent (#\infty# ) ?
#\intx^5\ln(x)dx#
My answer:#x^6/6(\ln(x)-1/6)+C# #\int\sec^3(x)\tan(x)dx#
My answer:#1/3\sec^3(x)+C# #\int(x^3)/(x^2+1)dx#
My answer:#x^2/2-2\ln|x^2+1|+C# #\int(5x)/(x^2-3x)dx#
My answer:#5\ln|x-3|+C# - Find the area of the region bounded by
#y=4-x^2# and#y=2x+1# .
My answer:#27/3# - Find the volume of the region bounded by
#y=x^3# ,#y=0# , and#x=3# , revolved around the y-axis.
My answer:#(243\pi)/5# - Approximate
#\int_2^4\sqrt(x-2)dx# using the Trapezoidal rule, rounding to 4 decimal places.
My answer:#\approx1.8195# #\int_1^\infty(\tan^-1(x))/(x^2+1)dx#
My answer: divergent (#\infty# ) ?
1 Answer
Mar 20, 2018
1 - 4 check by differentiating.
Explanation:
5) is incorrect
6) I get the same answer
8) converges