(x² – 9) dx

Q: (a) [z. ells dr

A:

Q: Define the following improper integrals integral - infinity to infinity f(x) dx

A:

Q: Evaluate the following integrals using integration by parts. Sre* dx f x3 In x dx -2x sin 2x dx

A: Solve the following

Q: Evaluate the following integrals using theFundamental Theorem of Calculus.

A:

Q: (а) In each part, evaluate the integral, given that f(x) = 2, | 2х, х 1 (a) f(x) dx (b) f(x) dx 10…

A: Given,f(x)=2x when x≤1f(x)=2 when x>1a)∫01f(x)dx=∫012xdx;                       (here limit of…

Q: V1+r+dydr.

A: First we calculate integration of dy then dx. See 2nd ,3rd and 4th step.

Q: Use the form of the definition of the integral given in the theorem to evaluate the integral. La (12…

A: According to the given information, it is required to evaluate the integral.

Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's rule to approximate the integral In(x) dx…

A: We use trapezoidal rule ,midpoint rule,simpson's rule to approximate the given integral

Q: use a definite integral to find the area of theregion between the given curve and the x-axis on the…

A:

Q: Evaluate the following integrals using theFundamental Theorem of Calculus.

A:

Q: Q2/ Evaluate the following integrals by using Tow – points Gaussain Quadrature So 1+x dx

A: In this,we find the value of the integral by using two points gaussian quadrature formula.

Q: Evaluate the integral by making an appropriate change of variables. 9(x dA, where R is the rectangle…

A:

Q: Use the form of the definition of the integral given in this theorem to evaluate the integral. dx

A:

Q: Use the trapezoid rule to approximate the following integrals: (using n = 4 subintervals) a.…

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: use a definite integral to find the area of theregion between the given curve and the x-axis on the…

A: Given curve: y=πx2 Concept used: The area between a curve fx and the x-axis on an interval a, b…

Q: Use an appropriate contour integral to evaluate the following real integral rinfinity (26 – 8)dx Jo…

A: Given, integral is as, ∫0∞x6-8x4+5x+42dx  I=12∫-∞∞x6-8x2+12x2+42dxconsider…

Q: Calculate the following integrals, assuming that | f(x) = 1, f(x)dx = 4, | f(x)dx = 7 0. 7. %3D

A: The solution is given below:

Q: Define the following improper integrals integral - infinity to 0  f(x) dx

A: Given: The improper integrals f(x)dx from limit -infinity to zero.

Q: Estimate the following integral using the trapezoidal rule with n=10. 5² = 1+x² dx

A:

Q: Evaluate the integral by interpreting it in terms of areas. La '5 (1 – x) dx

A: The solution is:

Q: Q2) By using a division method. Evaluate the following integrals: y?tan-'ydy

A: To find the integration

Q: use a definite integral to find the area of theregion between the given curve and the x-axis on the…

A: Given that : The equation of the curve is y = x2 + 1 .

Q: Which of the following integrals will find the area of the surface generated by revolving the curve…

A: If y=fx is a continuous function on the interval a, b then the area generated by rotating the curve…

Q: Evaluate the integral by first modifying the form of the integrand and then making an appropriate…

A:

Q: (b) x-2º dr

A:

Q: Which of the following integrals correctly gives the area of the region consisting of all points…

A: Topic = Area Correct option = A

Q: dx ax + b

A:

Q: Evaluate the integral by interpreting it in terms of areas.

A: At first we draw the graph of given function:

Q: 3. Evaluate the following integrals. Show how you find your bounds of inte- gration. 1 (a) dzdydr 1²…

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Find the following indefinte integrals (most general antiderivatives): a. Integral sign…

A:

Q: Evaluate the following integrals using (a) Trapezoidal Rule and (b) Simpson Rule by finding n such…

A:

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

A:

Q: Evaluate the following integrals using theFundamental Theorem of Calculus. Sketch the graph of the…

A: To evaluate  ∫-23x2-x-6dx

Q: Evaluate the following integrals using theFundamental Theorem of Calculus. Sketch the graph of the…

A: Given integral ∫1221-1x2dxwe have to evaluate the given integral using the fundamental therorem of…

Q: Evaluate the following integrals using theFundamental Theorem of Calculus. Sketch the graph of the…

A: Given integral, ∫01x-xdxwe have to evaluate the given integral using the fundamental theorem of…

Q: 2. In each part, use a definite integral to find the area under the curve y= f(x) over the stated…

A: We have to find the area of the given functions over the given interval using definite integral.

Q: Which of the following integrals represent the area between the curves y=xy=x and y=x3y=x3? Hint:…

A:

Q: Use a definite integral to find an expression that represents the area of the region between the…

A:

Q: Use the trapezoid rule to approximate the following integrals: (using n = 4 subintervals) a.…

A: We have to find the integral using trapezoidal rule for n=4. I=∫02(2x3+3x2-1x)dx

Q: Evaluate the following integral, where R is bounded by x= 2, y = 3x + 3, and y = -x- 1. y? dA R

A: We can think of this region as y ranging from -x - 1 to 3x + 3. and x ranging from -1 to 2.

Q: Evaluate the following integral using the fundamental theorem of calculus. Sketch the graph of the…

A: We have to evaluate the integral.

Q: use a definite integral to find the area of theregion between the given curve and the x-axis on the…

A:

Q: Evaluate the following integrals using theFundamental Theorem of Calculus.

A: the given integral is: ∫12z2+4zdz we have to evaluate the given integral.   let the given integral…

Q: Evaluate the following integrals using theFundamental Theorem of Calculus.

A: We have to evaluate integral A = ∫π/43π/4cot2x +1 dx Using Fundamental theorem of Calculus,( F is…

Q: Use the form of the definition of the integral given in the theorem to evaluate the integral. (x? 4x…

A: We can find the solution

Q: Which of the following integrals represent the area enclosed by the smaller loop of r = 1 +2 sin 0?

A:

Q: Evaluate the integral by naking the given substitution. Use C for the constant of integration) a* dx…

A:

Q: Compute the indicated integral by findng the area of the trapezoidal figure below. 110 4,0 F1 10 •5…

A: Given: A=∫35x+3dx

Q: Evaluate the integral using the following values. 9. x3 dx = 320, J2 x dx = 16, dx = 4 %3D r2 x3 dx

A: Given: I=∫22x3dx We know that ∫aafxdx=0                                                     ..1

Q: Evaluate the following integrals using theFundamental Theorem of Calculus.

A: We have to evaluate the integral using fundamental theorem of calculus: ∫0ln8ex dx We know the…