9. Demonstrate the method of the Fundamental Theorem of Calculus to find the following definite integrals..Show all work. (a) (3x - 5)?dr

Q: r sin(T|2² - 1) cos² (7|2² - 11) da -3

A: To find the following definite integral.

Q: X (sinx 16)-()35in (ux) 13) 2020 +1 13

A:

Q: 02: Let f(x)= x' – 7x+ 2, 0sxs1. 1. Show that f(x) has exactly one real root in the indicated…

A: Answer

Q: Use the Fundamental Theorem of Calculus to evaluate the following definite integral. V3 2 8 dx V1-x?

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Q: (s) [₂ x sin(x² - 1) cos(x² − 1) + 1 dæ -1

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Q: Does the function listed below have any points where the tangent is horizontal? If so, find the…

A: If the tangent is said to be horizontal then the slope of the tangent at the point is zero.  Slope…

Q: → (+,-) (- -) J (4)

A:

Q: 3. Use the fundamental theorem of calculus to find the exact value of the definite integral. Show…

A: Definition used -                 Power rule of integration -                       ∫xndx…

Q: W) Find the definite integral.

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Q: J Te 1 (3 − 2x(1 – 3x)) dr. - - π/2 π/4 dä. / (√x - √/12) dz √ 2² v x²√x³+3 dx [(sec² (r) - csc²…

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Q: =) Which of the following functions are and /or IZI> 2: हन ii) 2²1 Z-√2+4 analytic in IZK< 2

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Q: Evaluate the definite integral of the algebraic function. Use a graphing utility to verify your…

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Q: (ii) Evaluate the definite integral r³e² dr.

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Q: Q.2 If f(2)=zsinz, evaluate the real and imaginary parts of f2) and determine whether the function…

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Q: X (sinx)dx xp(xu!s) )c) 35in (ux) 2020 +1 13.

A: For (1),   ∫33xπsinxdxNote that ∫aafxdx=0, a≠∞. So, =0

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.