1 ex SS 4dydx 0 1

Q: A tank initially holds 40 gallons of a brine solution containing lb of salt per gallon. At t = 0,…

A: We will form differential equation for amount of salt in the tank and then solve it to get amount…

Q: ot) Evaluate the integral 9 L₁ (1x) — 4) da (|x|- dx - -7 using the net area of a region. Give the…

A: Here we have given an integral:

Q: r = 4cos0 COS

A: The region bounded by the curve r= 4 cos θ is as shown:

Q: Solve by integration: A region is bounded between x=0, y=1, x=1, and y=(x-1)^2+1. What is the…

A:

Q: sketch the region of integration, reverse the integral and evaluate 4-x 2 23 4-9

A: Consider the provided question,

Q: a) Reduce the integral to the repeated integral and show limits of integration. b) Calculate the…

A:

Q: 3. tind the area bounded by thu follo wing curves: y= X^2-4,y= 0,x = 4

A:

Q: Solve the area bounded by y3 + 10y + 5 = x², the y-axis and the lines y=0 and y=3 *

A: Given:  The boundary curve1. y3+10y+5 = x2  OR x = ±y3+10y+5 2. y=03. y=34. x=0 y-axisThe given…

Q: SOLVE STEP BY STEP Sketch the region bounded by the curves y = vx + 4 , y=x+2 and evaluate the area.

A: the given curves are: y=x+4 and y=x+2. we have to skecth the region bounded by the given curves and…

Q: For the region bounded by x + y² = 20 and x + y = 0, decide whether to integrate with respect to a…

A: The given problem is to find the area of region bounded by given curves x+y2=20 and x+y=0.

Q: change the order of integra tion and hence evalugte

A: The given integral is: ∫04∫28-yx+y dx dy The limit of x changes from x=2 to x=8-y. The limit of y…

Q: Givm trapgoidal rule with h =0.25 by Using apploximate the integral.

A: The solution is Given as

Q: 1 ✓ Find the area of the region bounded above by y bounded below by y=x² and bounded on the sides by…

A:

Q: When x=-y2 and y=x+12, draw the graph and let the​ region's area as an iterated double integral,…

A:

Q: Using double integration, find the area for x > 0 that is enclosed by the y-axis, the curve y =…

A:

Q: find: The center of the area for the shaded region.

A: We are given with function and find the area of the shaded region

Q: Use integration to find the area of the triangular region having the given vertices. (0, 0), (8, 0),…

A:

Q: | x√x + 1dx|

A: Use integration by partsSubstitute

Q: Use integration to find the area of the figure having the given vertices. (0, 0), (1, 6), (3,-2),…

A: We will find the area of the figure having the given vertices.

Q: Find the value of a and b if the curve +b) touches the x-axis at x=2 and line y=2x at the origin.…

A: Given curve is y=x(x-2)(ax+b) The curve touches x-axis at x=2 and the line y=2x at the origin. The…

Q: Q1\ sketch the region of integration and write an equivalent double integral and evaluate the…

A: First we write the regions of given integration and the we draw a diagram. Next we apply the…

Q: Find the area of the region bounded by = y ; x=2y²_4

A: The given functions are x=y2 and x=2y2-4 To find the area enclosed between the curves.

Q: Consider the shaded region between the curves z = f(y) and r g(y) in the image below. %3D - () (3,2)…

A: Topic :- Application of integration