Question

Evaluate the integral.

π/2 | sin^{5}(θ) cos^{5}(θ) dθ |

0 |

Answer #1

Evaluate, in spherical coordinates, the triple integral of
f(ρ,θ,ϕ)=cosϕ, over the region 0≤θ≤2π, π/6≤ϕ≤π/2, 3≤ρ≤8.
integral =

Evaluate the integral: ∫23√x2−4x4dx
(A) Which trig substitution is correct for this integral?
x=4sec(θ)
x=4tan(θ)
x=23sin(θ)
x=2sec(θ)
x=2tan(θ)
x=2sin(θ)
(B) Which integral do you obtain after substituting for x and
simplifying?
Note: to enter θ, type the word theta.
∫ dθ
(C) What is the value of the above integral in terms of θ?
+ C
(D) What is the value of the original integral in terms of x?
+ C

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

a.
r=3 - 3cos(Θ), enter value for r on a table
when;
Θ=0, (π/3),(π/2),(2π/3),π,(4π/3),(3π/2),(5π/3) & 2π
b. plot points from a, sketch graph
c. use calculus to find slope at (π/2),(2π/3),(5π/3)
& 2π
d. find EXACT area inside the curve in 1st
quadrant

If θ is in the interval [0, 2π) and cos(θ) = √ 2/2 , then θ must
be π/4 .
State true or false.

conducting cones (θ = π/10 and θ = π/6) of infinite
extent are separated by an infinitesimal gap at r = 0. If V(θ =
π/10) = 0 and V(θ = π/6) = 50 V, find V and E between the cones.
Solution:

Evaluate the integral: ∫8x^2 / √9−x^2 dx
(A) Which trig substitution is correct for this integral?
x=9sec(θ)
x=3tan(θ)
x=9tan(θ)
x=3sin(θ)
x=3sec(θ)
x=9sin(θ)
(B) Which integral do you obtain after substituting for x and
simplifying?
Note: to enter θθ, type the word theta.
(C) What is the value of the above integral in terms of θ?
(D) What is the value of the original integral in terms of x?

3.5.2a. If csc(θ)=3 and (π/2) <?θ< ?π ( signs are less
than and equal to) find the
following and give exact answers:
(a.) sin(θ)
(b.) cos(θ)
(c.) tan(θ)
(d.) sec(θ)
(e.) cot(θ)

use residues to evaluate the definite integral
integral (0 to 2 pi) ( d theta/ ( 5 +4 sin theta))

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

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