(3x – 8)² dx = f(u) du where u = (enter a function of æ) du = da (enter a function of æ1) a= (enter a number) b= (enter a number) f(u) = (enter a function of u). The value of the original integral is

Q: Find the Particular Integral for the given differential equatiorn d²y dy +3- dx +6y =2x²+x+5 dx2…

A: using expansion,         (1+x)-1 =1-x+x2 -x3+...

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Q: 1. Find the following integrals. i) S 3e-2x dx 2x2-1 dx ii) S: 2x3-3х

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Q: 4. Evaluate the given integral. |(x + 1)(x – 3)| dx -2

A: Solution:Given∫-20(x+1)(x-3)dx =∫-20(x2-2x-3)dx= ∫-20(x2-2x-3)dx= x33-2x22-3x0-2=0--83-4+6=23

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Q: 3. 'Evaluate the integral. 5 dx х0.2

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Q: Find the indefinite integral. 1. 16 + t² dt * (x² + 4)³/2 + 4)3/2 2. -dx-

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

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A: Given,           ∫abfxdx=∫-28fxdx+∫810fxdx-∫-25fxdx

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A: Given information:-

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A: Use substitutions to integration

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A: given equation= e5x+6

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A: Recall: Slope intercept form of an straight line:         y-y1=y2-y1x2-x1x-x1

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A: I have stated the used formula in the solution

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A: We have to evaluate to integrate

Q: find the indefinite integrals. 1. ∫ e−0.05t dt 2. ∫ (3/t  -  2/t^2)  dt

A: case 1:The given indefinite  integral  is ∫e-0.05t dt.Let u = - 0.05t, then du/dt = -0.05.

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A: Use by parts integration

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Q: 13. Find the integral using the u substitution method Jx(x+1)*dx

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A: To evaluate the given integral

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Q: • 1/2 3x2 Calculate the integral: dx 3/2 (1 – x²) 2 0. а) О3/3 + 2 b) O v3 2 V3 - 6 d) O v3 + n e)…

A: This question related to integration.

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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.