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Calculus
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13 Nov 2019

1. Evaluate R y(x) dx (that is, the indefinite integral, or the anti-derivative) for the following y(x):

(a) 5x^2/3

(b) 2(x − 1)^−2

(c) sin(2x − 1)

(d) 3e^−2x

(e) (x − 2)^−1

(f) 2x−1/x+1

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Collen Von
Collen VonLv2
10 Aug 2019

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Related questions

Evaluate the indefinite integrals.

(a) Z (√x/2 + 2/√x) dx

(b) Z (2 cos 2x − 3 sin 3x) dx

4. Use the substitution method to evaluate:

(a) ∫ xsin(3x^2 + 1) dx

(b) ∫ sin^3 x dx

(c) ∫ (3x^2 − 1)(2x^3 − x)^−3 dx

Now you'll evaluate the integral ∫C6ysin(2x)dx+5xydy ∫ C 6 y sin ⁡ ( 2 x ) d x + 5 x y d y on the closed curve C consisting of the line segments from (0,0) to (5,1) to (0,1) to (0,0) using Green's Theorem. Green's Theorem says this integral can be rewritten in the form ∫∫Df(x,y)dA ∫ ∫ D f ( x , y ) d A In this integral, f(x,y) =

Setting up the double integral over the region D, you get

∫BA∫DCf(x,y)dxdy∫AB∫CDf(x,y)dxdy


(Note that the order of integration is specified--for this integral it will turn out that this is the easier order of integration). In this,
A =

B=

C=

D=

Evaluting this integral,
∫C6ysin(2x)dx+5xydy=∫∫Df(x,y)dA=∫C6ysin⁡(2x)dx+5xydy=∫∫Df(x,y)dA=

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