Calculus Answers

Evaluate the following integral by first converting to an integral in polar coordinates.
∫
0
−
2
∫
√
4
−
y
2
−
√
4
−
y
2
x
2
d
x
d
y
∫−20∫−4−y24−y2x2dxdy

Use Weierstrass’ M-Test to prove that the series ∑(x^nXn^2)
∞
n=1

n converges uniformly in x
the interval .
(0,1/5)

Use Weierstrass’ M-Test to prove that the series ∑(x^nXn^2)
∞
n=1

n converges uniformly in x
the interval .
5
1
,0



[img]https://upload.cc/i1/2020/04/20/RAD7Mo.jpg[/img]


question is in picture,R=4

Find the indefinite integral of the following functions
Y= 3t^2+2e^3t+1/t+ cos 3t
Y=x/2+3x^2

Find the sum of the x and y intercept of any tangent line to the curve √x + √y = √k

[img]https://upload.cc/i1/2020/04/18/6EeNfM.jpg[/img]


question in photo,R=4

Integrated ×^2+×+5/(×^2+4)(×+1) dx.
Integration by part

two boat each move a velocity v relative to the water and both cross a river of breadth a running with uniform velocity V.they start together one boat crossing by shortest path and the otherin shortest time.find the difference between the time of arrival.