x for -100 sxs100 5. J(x)3D for |x] > 100

Q: 21. f(x) = In (5-3x²)' J6x² + 21. f(x)= In| (5-3x V6x? + 8х —12 1+5t 22. f(t)= In(t)

A: As per our guidelines, I can answer maximum one question. Since you have asked for multiple…

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A: To find The anti derivative of f(x).

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Q: b) I =f- x(1+(In x))

A:

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A:

Q: 2 3x 2. Evaluate f x'e* using integration by parts.

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Q: find the critical points:

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Q: Find an antiderivative F(x) with F'(x)=f(x)=7+18x2+14x6 and F(1)=0.

A: Find an antiderivative F(x) with F'(x)=f(x)=7+18x2+14x6 and F(1)=0.

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A: The given function, f(x)=x3

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A:

Q: At what interval is y=3x5-5x3 decreasing O x>1 O -1<x<0 O -1<x< OU 0<x<I O -1<1<l

A: We have to find interval where it is decreasing

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Q: Find an antiderivative of the function f(x)=1/x4.

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Q: 9. What is the antiderivative of f (x* – x³ + x² ) dx? - 1 r5 а. 5 1 1 --x4 +x³ +1 4 -3 с. X. 4 3 b.…

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Q: der to evaluate t son's 1/3rd rule e used at x = 0.C of the error of

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Q: 2. Find the most general antiderivative of f(x) = 3+22 %3D

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Q: Evaluate the integral. S2 15 - x2 if o < xs 3 3 if -3 sx S0 f(x) dx where f(x) = %3D

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Q: 4 + 9x is x2 The antiderivative of the function f(x) %3D

A:

Q: 2. Consider the three functions below: S(z) = 2z S(z) =r S(x) = 2"

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Q: 1. For the function f(x)= x³ +5x²+2x-8, explain how you determine which integral values of x you…

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Q: Find an antiderivative of the function f(x)=1/3√x.

A:

Q: 3. Find the general antiderivative of f(x) = x² + 3x+4 sinx.

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Q: Find f fy. - f(x.y.z) = x - Vy² + 22? + 2z² = (Type an exact answer using

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Q: 1. f(x) = Vx - 1 at x = 5 %3D 2. f (x) = at x = 2 x-2

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Q: 10 Evaluate the integral f 2x (x2 + 4) " dx using the substitution u = x² + 4. 2x (x² + 4)*" dx =|…

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Q: Find f(3,4) for f (x, y) = ln(x + Vx² + y²).

A: We have to find out the derivative

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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.