Question

compute the definite integral. The integral of 0 to 1 x^4(1-x)^4/1+x^2 dx

Answer #1

1. Evaluate the definite integral given
below.
∫(from 0 to π/3) (2sin(x)+3cos(x)) dx
2. Given F(x) below, find F′(x).
F(x)=∫(from 2 to ln(x)) (t^2+9)dt
3. Evaluate the definite integral given
below.
∫(from 0 to 2) (−5x^3/4 + 2x^1/4)dx

Evaluate definite integral (0 to pi/2) secxtanx-sec^2(x) dx

definite integral 0 to 7 of e^(x)sin(x)dx

Evaluate the integral using trig substitution.
definite integral from 1 to sqrt(2) 6 / (x^2 sqrt(4-x^2))dx
(a) write the definition for x using the triangle
(b) write the new integral before any simplification
(c) write the new integral after simplifying and in the form ready
to integrate
(d) write the solution in simplified exact form
write all answers next to the specified letter above

1. the integral of 0 to 1 of (x) / (2x+1)^3 dx
2. the integral of 2 to 4 of (x+2) / (x^2+3x-4) dx

Use a power series to approximate the definite integral to 4
decimal places: from 0 to 1/2 (x^2)(e^(-x^2) dx. Find power series
of e^-x^2. and the value of the integral (how many terms
needed)

1. Integral sin(x+1)sin(2x)dx
2.Integral xe^x dx
3. integral ln sqrt(x) dx
4. integral sqrt(x) lnx dx

Evaluate double integral Z 2 0 Z 1 y/2 cos(x^2 )dx dy
(integral from 0 to 2)(integral from y/2 to 1) for cos(x^2) dx
dy

a). Find dy/dx for the following integral.
y=Integral from 0 to cosine(x) dt/√1+ t^2 ,
0<x<pi
b). Find dy/dx for tthe following integral
y=Integral from 0 to sine^-1 (x) cosine t dt

Use the definition of the definite integral to evaluate Integral
from 2 to 6 left parenthesis x squared minus 4 right parenthesis
dx.

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