:Find the Value af the integral COs Z d2 2(Z-7) 121=1 2. 22+1 COS Z JZ 3. 121=1 z (2-3)

Q: q dx (6x²+ 32) dz

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Q: Prove using the IVT cosx = cos-1x has a solution in (0, 1).

A: cos x = x   rearrange to x - cos x = 0

Q: Prove that J5/2(x) = 2 TCX CScanned with CamScanner 3-x² 2 sin x - 3 COS X

A: Use the given information.

Q: d) fe'cos( 41)

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Q: Solve the definite integral using usub

A: To integrate,

Q: Prove that 1 3V2 dx < 3 + x (Hint: Theorem 5.9(ii) and carefully chosen functions should do the…

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Q: -2 cos(6t) dt J (10+4 sin(6t))²

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Q: Evaluate the definite integral 8 | (18a? – 8x + 3) da

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Q: HELP EVALUATE THE INTEGRAL

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Q: 8a + 20x dr. x* + 5x² + 6 Evaluate the definite integral

A: We can evaluate the integral as below.

Q: Integrate fx Sx O cos(4x) dx (sin(4x) - x sin(4x)) + C cos(4x) + 4x sin(4x) + С (4x sin(4x) +…

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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.