Question

**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

Answer #1

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

1) Find the net change in f(x) on 0≤x≤3 where:
f'(x)=(x^3)/√(36−x^2) Express your answer in exact form.
2) Evaluate the definite integral from 3 to √18:
∫(√9√(x(squared)−9)/x dx
3) Compute the given integral. ∫√(x(squared)-9)

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

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

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.Find ff if
f′′(x)=2+cos(x),f(0)=−7,f(π/2)=7.f″(x)=2+cos(x),f(0)=−7,f(π/2)=7.
f(x)=
2.Find f if
f′(x)=2cos(x)+sec2(x),−π/2<x<π/2,f′(x)=2cos(x)+sec2(x),−π/2<x<π/2,
and f(π/3)=2.f(π/3)=2.
f(x)=
3.
Find ff if f′′(t)=2et+3sin(t),f(0)=−8,f(π)=−9.
f(t)=
4.
Find the most general antiderivative of
f(x)=6ex+9sec2(x),f(x)=6ex+9sec2(x), where −π2<x<π2.
f(x)=
5.
Find the antiderivative FF of f(x)=4−3(1+x2)−1f(x)=4−3(1+x2)−1
that satisfies F(1)=8.
f(x)=
6.
Find ff if f′(x)=4/sqrt(1−x2) and f(1/2)=−9.

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

Pat made the substitution x
−
3 = 2sin
t
in an integral and integrated to obtain
f(x)
dx
= 9t
−
2 sin
t
cos
t
+
C
.
Complete Pat's integration by doing the back substitution to find
the integral as a function of
x.
f(x) 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

Instructions: For each region described, set up, BUT DO NOT
EVALUATE, a single definite integral that represents the exact area
of the region. You must give explicit functions as your integrands,
and specify limits in each case. You do not need to evaluate the
resulting integral.
1. The region enclosed by the lines y=x, y=2x and y=4.
2. The region enclosed by the curve y=x^2 and the line
y=5x+6.
3. The portion of the region inside the circle x^2+y^2 =4...

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