Use numerical integration to evaluate the following: dx (b) e-" sin y dy 2 x(x + 2)

Q: Evaluate the interated integral: LS-² x² sin(y) dy dx

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Q: Make an appropriate substitution and then use integration by parts to evaluate the integral. dx e

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Q: cos y dy sin² y + sin y – 6

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Q: Evaluate the integral. (Use C for the constant of integration.) | 3x2 cos(mx) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 10e-0.7x dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 10x2 cos(mx) dx

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Q: Supply the missing integrand and the limits of integration sinx dy dx _dx| 1– y² dx (x=1) dx

A: This question can be solved using the concept of double integration.

Q: Q2/ Evaluate the integral: 6. xe' dy dx by changing the order of integration.

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Q: evaluate the double integral ∫01∫y1 √1+x2 dxdy by changing the order of integration

A: In this question we will use basic of calculus i.e concept of double integration. We will change the…

Q: (b) Use Romberg integration to compute dx 1+x correct to three decimal places.

A: Given: I=∫01 dx1+x  correct to 3 deecimal placesLet h=0.25,…

Q: 5e5x dx

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Q: Change the order of integration and then evaluate the integral: ² x sin (x) dydx π/2 cx+1 1

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Q: Find the integral xn ln x dx; n ≠ −1, n real. (Use C for the constant of integration.)

A: we have to use integration by parts ∫uvd=u∫vd-∫du∫vdd  and ∫xndx=xn+1n+1+c where c is the…

Q: Evaluate the integral 0. e dx dy by reversing the order of integration. NOTE: Enter the exact…

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Q: Evaluate the integral. (Use C for the constant of integration.) 7 V 1- sin(x) dx

A: Evaluating the indefinite integral

Q: 32. Evaluate by changing the order of integration: sin y dy dx

A: Given that ∫04∫x2siny3dydx Here x=0 to x=4y=x to y=2

Q: Use the integration by parts to evaluate the integral. V3 2 sin-1 x dx 0,

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Q: evaluate using Integration by Parts.

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Q: how to solve problem in photo attached

A: Substitute x = t2 in the given integral and so the limit varies pi/2 to pi.

Q: Evaluate by changing the order of integration: IL sin y³ dy dx 0.

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Q: Reverse the order of integration and then evaluate the integral. 5 5 sin y dy dx 0 x

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Q: Evaluate the integral. (Use C for the constant of integration.) 3,2r+e2" dx

A: Solve the intregal

Q: Find the integration by applying (by part method) f Sin-¹y dy

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Q: Evaluate the integral. (Use C for the constant of integration.) 9x cos(8x) dx

A: Integrate this by integration by parts

Q: Please determine the approximate integration using excel. ⌠13 (e0.5x + sin2x)dx, use n=4

A: Let,I=∫13e0.5x+sin2xdxI=e0.5x0.5+-cos2x2+CI=2e0.5x-cos2x2+C

Q: First make a substitution and then use integration by parts to evaluate the integral. ecos t sin 2t…

A: The definite integral to be solved is  ∫0πecostsin2tdt

Q: Evaluate the integral. (Use C for the constant of integration.) 3e3x dx

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Q: dx dy be a double integral. What will be the equivalent expression if the order of integration is

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Q: Evaluate the integral. (Use C for the constant of integration.) 7 dx x(x* + 1)

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Q: Evaluate the integral. (Use C for the constant of integration.) 7 cos(TX) cos(4Tx) dx

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Q: Evaluate the integral r4-x2 8x cos y dy dx r2 y – 4 by reversing the order of integration.

A: Evaluating the g8iven integral directly is not easy. So if we change the order of integration from…

Q: Reverse the order of integration and then evaluate. a. S S, x² sin(xy)dxdy

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Q: Evaluate the integral. (Use C for the constant of integration.) COS s-1(x) dx

A: Let arccos(x)=t x=cos(t) dx=-sin(t)dt So the integral becomes - int t sin(t)dt =-t int sin(t)dt+int…

Q: Evaluate the integral. (Use C for the constant of integration.) 2 tan3(x) sec(x) dx

A: Let sec(x)=t sec(x)tan(x)dx=dt tan2(x)=sec2(x)-1 Substituting we get 2 int (t2-1)dt =2 (t3-t)+C…

Q: First make a substitution and then use integration by parts to evaluate the integral. ecos(t)…

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Q: Reverse the order of integration and evaluate the integral. 1 1 dy dx + 1 0 4x

A: ∫01∫x1x2y7+1dydx⇒∫0=x1=x∫x=y1=yx2y7+1dydx The reversed order of the integration is…

Q: Evaluate the integral 2 sin(x dy by reversing the order of integration. With order reversed, sin(x…

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Q: sin(e" – y) dy dx - In x

A: We have to find integral given in question.

Q: e for (2x + 1) cos(x) dx. 14. Use integration by parts to evaluate

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Q: Evaluate the integral dx dy by reversing the order of integration. NOTE: Enter the exact answer. e…

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Q: Evaluate the integral. (Use C for the constant of integration.) 4e2x dx 5 + ex

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Q: Evaluate the integral. (Use C for the constant of integration.) cos−1(x) dx

A: Use the method for integration by parts to determine the given integral. I=∫cos−1xdxLet…

Q: Q4- BY usin simpson rule for integration find J=Jo' e* dx. n=10

A: J=∫01e3xdx.   N=10 f(x)=e3x h=b-aN h=1-010=0.1 The value of table for x and y x 0 0.1 0.2 0.3 0.4…

Q: a. Sx² e3*dx b. St sin t dt

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Q: (i) Change the order of integration in the integral vi-x dx dy and hence evaluate.

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Evaluate the integral. (Use C for the constant of integration.) 9e 9x dx

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Q: Evaluate the integral. (Use C for the constant of integration.) cos-1(x) dx

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Q: Evaluate the double integral: ¹ sin(x³) Lo Sc vy vy (Hint: Change the order of integration to dy…

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Q: Use integration by parts to evaluate the integral: for 9t sin(t)dt

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.