Question

For t ≥ 0, let (cosht,sinht) be the point sitting on the curve xˆ2−yˆ2 = 1...

For t ≥ 0, let (cosht,sinht) be the point sitting on the curve xˆ2−yˆ2 = 1 in the first quadrant. Let L be the line connecting the origin to this point.

(a) Find the equation of the line L.


(b) Set up an integral A(t) that computes the area of the region in the first quadrant bounded by the line L,the curve xˆ2−yˆ2 =1,and the line y=0.


(c) Simplify A(t) as much as possible. Hint: There should be one term you do not know how to

integrate, so you should leave this as an integral.

(d) Find A′(t), the derivative of A(t) with respect to t. (e) Use part (d) to determine that A(t) = (1/2)t.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Please feel free to ask doubts in the comment section and give it a thumbs up if you liked the answer. have a good day ahead.

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let R be the region of the plane bounded by y=lnx and the x-axis from x=1...
Let R be the region of the plane bounded by y=lnx and the x-axis from x=1 to x= e. Draw picture for each a) Set up, but do not evaluate or simplify, the definite integral(s) that computes the volume of the solid obtained by rotating the region R about they-axis using the disk/washer method. b) Set up, but do not evaluate or simplify, the definite integral(s) that computes the volume of the solid obtained by rotating the region R about...
Let C be a closed curve parametrized by r(t) = sin ti+cos tj with 0 ≤...
Let C be a closed curve parametrized by r(t) = sin ti+cos tj with 0 ≤ t ≤ 2π. Let F = yi − xj be a vector field. (a) Evaluate the line integral xyds. C (b) Find the circulation of F over C. (c) Find the flux of F over C.
1- Find the area enclosed by the given curves. Find the area of the region in...
1- Find the area enclosed by the given curves. Find the area of the region in the first quadrant bounded on the left by the y-axis, below by the line   above left by y = x + 4, and above right by y = - x 2 + 10. 2- Find the area enclosed by the given curves. Find the area of the "triangular" region in the first quadrant that is bounded above by the curve  , below by the curve y...
Let R in the x,y-plane be in the first quadrant and bounded by y=x+2 and y=x2,...
Let R in the x,y-plane be in the first quadrant and bounded by y=x+2 and y=x2, and x = 0. Find the volume generated by revolving the region R about the line x = 4.
Find the volume of the solid generated by revolving the following region about the given axis....
Find the volume of the solid generated by revolving the following region about the given axis. The region in the first quadrant bounded above by the curve y=x^2, below the x-axis, and on the right by the line x=1, about the line x=-4. Use the washer method to set up the integral that gives the volume of the solid.
With the parametric equation x=cos(t)+tsin(t), y=sin(t)-tcos(t) , 0 ≤ t ≤ 2π) Find the length of...
With the parametric equation x=cos(t)+tsin(t), y=sin(t)-tcos(t) , 0 ≤ t ≤ 2π) Find the length of the given curve. (10 point)     2) In the circle of r = 6, the area above the r = 3 cos (θ) line Write the integral or integrals expressing the area of ​​this region by drawing. (10 point)
1) Set up, but do not evaluate, an integral to find the volume when the region...
1) Set up, but do not evaluate, an integral to find the volume when the region bounded by y=1, y=tanx and the y-axis is rotated about the following lines: a) The x-axis b) The y-axis c) The line y=2 d) The line x=3 e) The line x= -1 2) Set up, but do not evaluate, an integral to find each of the following: a) The volume that results when the region in the first quadrant bounded by y=sinx, y=1 and...
2. Consider the line integral I C F · d r, where the vector field F...
2. Consider the line integral I C F · d r, where the vector field F = x(cos(x 2 ) + y)i + 2y 3 (e y sin3 y + x 3/2 )j and C is the closed curve in the first quadrant consisting of the curve y = 1 − x 3 and the coordinate axes x = 0 and y = 0, taken anticlockwise. (a) Use Green’s theorem to express the line integral in terms of a double...
Consider the parametric curve x = t2, y = t3 + 3t, −∞ < t <...
Consider the parametric curve x = t2, y = t3 + 3t, −∞ < t < ∞. (a) Find all of the points where the tangent line is vertical. (b) Find d2y/dx2 at the point (1, 4). (c) Set up an integral for the area under the curve from t = −2 to t = −1. (d) Set up an integral for the length of the curve from t=−1 to t=1.
1. (1 point) For the curve given by r(t)=〈−7t,−4t,1+7t2〉r(t)=〈−7t,−4t,1+7t2〉, Find the derivative r′(t)=〈r′(t)=〈, , , 〉...
1. (1 point) For the curve given by r(t)=〈−7t,−4t,1+7t2〉r(t)=〈−7t,−4t,1+7t2〉, Find the derivative r′(t)=〈r′(t)=〈, , , 〉 Find the second derivative r″(t)=〈r″(t)=〈 Find the curvature at t=1t=1 κ(1)=κ(1)= 2. (1 point) Find the distance from the point (-1, -5, 3) to the plane −4x+4y+0z=−3.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT