Using integration by substitution in fx (x6- 2) dx, what is du? A. x5dx B. 6x5dx C. (x6- 2)dx D. x5(x6 - 2) dx

Q: Question -2x2 + 4x dx J (x² + 1)(x² – x)

A: Given: ∫-2x2+4xx2+1x2-xdx

Q: integration 1. Sx sec? 2xdx

A:

Q: dx x Vx²+2x-1

A: In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or…

Q: 19x + 87x2 -) dx (Use Term by term integration) O (38x + 58) Væ + C O (38 + 58 /æ)V¤ + C O (38 +…

A: Given :                      ∫19x + 87x2xxdx

Q: 26. Solve using integration by parts f x*e-3* dx. Show your solution

A:

Q: 2x2-3х-1 -dx (x²+9)(x-5) E. Integrate:

A: Let's integrate.

Q: 25. Solve using integration by parts f x² Vx – 1 dx. Show your solution.

A:

Q: Question Using integration by parts, the integral f(9x 3)e*dx is equal to:

A: Given: ∫(9x-3)e3xdx Integration by parts: ∫uv dx=u∫v dx-∫dudx∫v dxdx Where, v and u functions of x

Q: (a) Calculate: S(5x + x 2) dx 3x2-2x (b) Evaluate: x3-x2+3 dx demonstrating the technique of…

A: The given integral is ∫5x3+x-2dx and ∫123x2-2xx3-x2+3dx The integral is defined by a limiting…

Q: Evaluate. (Use C for the constant of integration.) /x* - x³ + 64 x4 + 8x2 dx

A: Given,          ∫x6-x3+64x4+8x2dx

Q: Evaluate the integral. (Use C for the constant of integration.) (8x3 − 6x2 + 8x +

A:

Q: Using integrating factor, solve dy/dx - 2xy = x

A: The objective is to solve the differential equation dydx-2xy=x.

Q: dx x² Vx²-1 -2.

A:

Q: II. Perform the integration. 2х + 1 dx x2 + 8x + 25 2.

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Q: e2 6. - dx -Find 1

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Q: integral r5 dx V(5 – 2)3 MANUSIA

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Q: 3-x Evaluate I = . -dx Vx-2°

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Q: x³ +2x .3 dx x2+1

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Q: Using basic rules of integration, find a. dr b. Jrdx c. fx'(-2r² - 8)dx 12x² – x d. xp- -dx 1-3х e.…

A:

Q: s x3 √1-x² V dx

A: Given: I=∫x31-x2dx   ...1   As we know that; The Power rule; ∫xndx=xn+1n+1+C

Q: Evaluate the definite integral using the given values

A: Given: verify that ∫26x3dx=320 for verifying given integral we solve left hand side

Q: On the interval [-3, 3] (x², x) = / dx = 1 ||x²|| = dx II

A:

Q: 3x? – 8x – 1 B Evaluate the integral x3 A dx using 4x2 – x + 4 4 x +1 1 3x2 8х — 1 dx = x3 – 4x2 x +…

A: Given:          ∫3x2−8x−1x3−4x2−x+4dx

Q: Transforming A B C D dx using miscellaneous substitution will yield to secx + 1 2-2z² -dz 1+z² z²+z…

A: Here, the given integral is: I=∫dxsec…

Q: ODE d²y dx² 1 -|> X dy xp ㅅ X² 1

A: We have to identify the type of the given differential equation. For this, we have to rearrange the…

Q: 3) dx Evaluate : J4x (x² - 3)° dx

A: Given that a integration and we solve by using general formula of integration. We know that…

Q: - 1x Xe dx

A: Given function is. Y = X²e^-3x dX. We can use integraion by parts to solve above.

Q: Integrate the function. 9-x dx, x< 3 x4 27x3 OA. (9 -x²) 3/2 (9 - x²) 3/2 O B. x3 + C (9-x²) 3/2 +C…

A: Recall: ∫ax+bndx=an+1ax+bn+1

Q: Using integrating factor, solve  dy/dx - 3y = 6

A: To find the solution of the differential equation.

Q: (a) Using integration by parts, find fx sin(2x - 1) dx. (b) Use substitution method to find x² 2x-1…

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Q: 2х -1 dx 2 V3– x+x²

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Q: Question * Using integration by parts, the integral f (9x-3)e3*dx is equal to:

A: We have to integrate

Q: x +3 b. dx x2 - 3х - 10 с. x³ In(x²)dx at LKnow Chart part 2

A:

Q: dx |x3 +1

A: Solution

Q: Using integration by parts, which of the following options is true x arcsec x dx ? xdx A. * Arcsec x…

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Q: Use integration by parts to derive a reduction formula for x"e dx. Use the result from part 1 to…

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Q: x* dx 4. JTai-x²)* -2)2

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Q: x3 dx Using integration by parts to solve J- V4-x2 and letting -÷x², then v = f(x) is U = - %3D

A: We use integration by parts

Q: Evaluate the integral. | (5x² + 8) e-"dx -33e + 18 -33e-1 + 18 -33e-1 – 18 33e-1+ 18

A: Given, ∫015x2+8e-xdx  We have to evaluate the integral.

Q: 4 Using integration by parts, what is an appropriate next step to solving (x?e*dx = 2xex - [x²e*dx…

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Q: 2x Evaluate dx using suitable technique. (x² +4)(2x-1)

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Q: integral. Give your answers as fractions 3 (i) dx V1- x2

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Q: Original Integral Rewrite Integrate Simplify x2 .3 X:X ) • x(x3 + 7) a dx + 7x) dx + C 10

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Q: 5. fx3* dx

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Q: Not sure how to start this problem.

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Q: Using Integration By Parts, x3 / x² + 4 dx = u v - v- Svau-

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Q: Evaluate using u-substitution j²x²√x²1 x²1 dx Evaluate using u-Substitution (Inx) 3 St dx x

A: 1. ∫12x2x3-1dx2. ∫ln x3xdx3. ∫2θ-5 cos2θ dθ

Q: Sa -1 dx (1+x²) 12/2

A: Given: ∫-11dx1+x232 To find: value of the integral ∫-11dx1+x232.

Q: 15. 1 dx V5x+4

A:

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.