Let R Be the Region in the First Quadrant

Now consider representing a region R with polar coordinates. Let R be the region in the first quadrant enclosed by the graphs of y y x2 as shown in the figure above.

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We can approximate this region using the natural shape of polar coordinates.

. The region described looks like this. Find the volume of the solid generated by revolving R about the x-axis by integrating with respect to x. C Find the volume of the solid generated when S is revolved about the x-axis.

Revolve R about the x-axis and use the disk method. Were given a transformation a region in the X Y plane and an integral and were asked to use this transformation to rewrite our integral as an integral over the appropriate region in the UV plane and to evaluate the integral over this region in the UV plane. Let R be the triangular region in the first quadrant with vertices at points 00 02 and 12.

Find the volume of a hemisphere of radius r in the following ways. Let R be the first quadrant region enclosed by the graph of y 2e-x and the line xk. R is in the region first quadrant with vertices.

Let R be the region in the first quadrant bounded by the x-axis and the graphs of y ln x and y 5x as shown in the figure above. Let R be the region in the first quadrant bounded by the graphs of y V9x and y Let V be the volume of the solid obtained by rotating R about the y-axis. Set up but do not evaluate an integral that will solve the problem.

B The region R is the base of a solid. Let R be the triangular region in the first quadrant with vertices at points 00 02 and 12. A Write an equation for the line tangent to the graph of f at 1.

The region R is the base of a solid. The region R is the base of a solid. Let R be the region in the first quadrant enclosed by the graphs of fxx83.

2x and b The region R is the base of a solid. 3 Let R be the region in the first quadrant bounded by the curve ysec 2x and the line y Suppose a tank that is full of water has the shape of a solid of revolution obtained by revolving region about the y-axis. Find the volume of the solid.

The equation of AB will be. Y-b b-0 x-0 0-a. Use the transformation x uv y uv with u 0 and v 0 to rewrite R y x x y d x d y iint _ R left sqrt frac y.

A Find the area of R. -ay ba bx. Find V by using washers.

Let R and S be the regions in the first quadrant shown in the figure. For the solid each cross section perpendicular to the y-axis is an isosceles right triangle with the right angle on the y-axis and one leg in the xy-plane. A Find the area of R b The region R is the base of a solid.

Portions of sectors of circles. Calculus questions and answers. B Find the area of S.

C Another solid has the same base R. What is the area of R. Let R be the region in the first quadrant of the xy-plane bounded by the hyperbolas xy 1 xy 9 and the lines y x y 4x.

Consider Figure 1431 a. Find the volume of the solid formed by revolving R about the x-axis. Up to 20 cash back Let R be the region in the first quadrant enclosed by y x2 y 2 x and x 0.

Let R be the shaded region in the first quadrant enclosed by the graphs of f and g. How much work is required to pump all the water to the top of the tank. The region R is the base of a solid.

V Find V by using cylindrical shells. A Find the area of R. Up to 24 cash back 4.

For this solid at each x the cross section perpendiculsr to the x-axis has area Ax sin. For this solid at each x the cross section perpendicular to the x-axis has area Ax sin x. 0 00 A a0 and B 0b from the image.

2 on a question Let R be the region in the first quadrant bounded by the graphs of xy3 and x4y as shown in the figure above. Find the area of R i. Th e region S is bounded by the y-axis and the graphs of and a Find the area of R.

Let f and g be the functions given by fx1sin2x and gxex2. For the solid each cross section perpendicular to the y-axis is an isosceles right triangle with the right. Let R be the region in the first quadrant bounded by the circle x 2 y 2 r 2 and the coordinate axes.

For this solid at each x the cross section perpendicular to the x-axis has area Ax sin pi2x. For the solid each cross section perpendicular to the x-axis is a square. Up to 20 cash back Let R be the region in the first quadrant enclosed by the graphs of y2x and yx2.

So the region are in the X Y plane is the first quadrant of the X Y plane bounded by the hyperbole as X y equals one x y equals nine. Find V by using washers. The region R is bounded by the x-axis and the graphs of yx2 3 and yxtan.

Given the data in the question and as illustrated in the image below. Let R be the region in the first quadrant that is enclosed by the graph of y tanx the x-axis and the line x π3 h. And gx x sin πas shown in the figure above.

Let R be the region in the first quadrant bounded by the graphs of y 9x and y Let V be the volume of the solid obtained by rotating R about the y-axis. Let R be the region in the first quadrant bounded by the curve. Write but do not evaluate an.

Y-b 0-a b-0 x-0 0 - ay -0 ba bx - 0 - 0 0. Find the volume of the solid. Let f be the function given by fxx34 - x23 - x2 3cosx.

Let R be the region in the first quadrant enclosed by the graphs of y 2x and y x2 as shown in the figure above. Calculus questions and answers. Assume x and y are in meters.

X b Find the area of R. A Find the area of R. B Region R is the base of a solid.

For this solid the cross sections perpendicular to the. C Another solid has the same base R. V Find V by using cylindrical shells.

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