Consider the area under one arch of the curve y(t) = 8sin(bt) for t≥0 where b is a positive constant. (a) Set up the definite integral needed to find the area. (b) Make an appropriate substitution. W = dw = dt (c) Write the definite integral in terms of w. (d) Evaluate the integral in part (c). dw

Q: Shade the region in quadrants I and IV which lies inside the curve r² = 8 cos (20) and outside the…

A:

Q: Find the area under the curve y X 29 from x 1 to x = t. Evaluate the area under the curve for t =…

A: To find the area under the curve .To evaluate the area under the curve for .To find the total area…

Q: Evaluate the integral: sec x(sec x + tan x) dx

A: To find the below integral.

Q: 1. f(x)=x²+2x+1 & f(x) = 2x+5

A: To find the area between the curve.

Q: let b be a constant. use definition to find  (integral 0 to b)(x+1)^2 dx.

A: Given: The expression of integral as ∫0bx+12dx, where b is a constant, To evaluate: The value of…

Q: sin³ x dx 7. Evaluate the integral:

A: Given:         ∫0πsin3x dx

Q: Evaluate  integral.

A: Let the given integral function be  ₀∫⁵(x4y+y)dx  First we have to separate into two integral terms…

Q: 1- x dx 21 y =

A: We solve the given integral using Trigonometry substitutions method.

Q: .2 /1+ x² dx

A: Explanation: Given that,  Let us assume Differentiate

Q: Prove 2 {y } = 5 2 {y} -y (o) the U definition of Laplace integral definition using transform: 2 {F…

A:

Q: Use integration by parts to find L[cos t]. Do not use et.

A: Laplace transform

Q: Set up but DO NOT EVALUATE an integral representing the area in one loop of the curve r = sin(30)…

A: Solve by using integration.

Q: Give an interval over which you could integrate to find the area of one leaf of the rose r = 2 sin…

A: r=2sin3θ

Q: Determine the indefinite integral J csch 2x dx.

A: To evaluate: ∫csch2xdx Let t=2x dtdx=2dt=2dxdt2=dx Integrating the given integral.…

Q: | 2°+Idal Vx² +1 dxl

A: The given integral is- ∫x3x2+1dx Let x2+1=u Differentiate w.r.t. x to both sides- 2x=dudxdu2=xdx…

Q: Let f(x) = -a² + 6æ – 5. Estimate the area below the curve y = f(x) and above the x-axis using 100…

A: Let f(x)=-x2+6x-5 To estimate the area below the curve y = f(x) and above the x-axis using 100…