Evaluate the indefinite integral. (80 +C %3D

Q: Find the following indefinite integral: ∫12x (x2 – 9 )-3 dx. Hint: Use a Substitution

A: Given: I=∫12xx2-9-3dx for evaluating given integral, we substitute x2-9=t…

Q: Determine the following indefinite integral.

A: First we separate the integral.

Q: 10 – 3x°dx_ Land de In (cose)

A:

Q: Find indefinite integral.

A: Given the indefinite integral ∫-u2-u2 du To evaluate the integral  Let I=∫-u2-u2 du

Q: Use substitution to find the indefinite integral. 6 10(1

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Q: Evaluate the definite integral two ways: first by a u-substitution in the definite integral and then…

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Q: Eva luate the integral and simplify S,"Inxdx 1. Sx'sinxdx 2.

A: We need to evaluate the integral: (A) I= ∫ lnx dx Integrating by parts: Using the formula: ∫ fg' =…

Q: Evaluate the following indefinite integral: - 5xvx dx

A: Given, ∫-5x x  dx   = ? ∫-5x x  dx   =   -5∫x3/2 dx…

Q: Evaluate the integral. X5/8 5/8 dx

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Q: 5. fe* di

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Q: Evaluate the indefinite integral: du + C.

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Q: Solve the integral( x is an exponent):

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Q: Evaluate the following indefinite integral. Do not include +C in the answer. 3 dx

A:

Q: V64 – x? da

A: Given: ∫64-x2xdx

Q: Evaluate the following indefinite integral. Do not include +C in your answer. |(-52° + 4)da

A:

Q: Find the indefinite integral

A:

Q: Evaluate the definite or indefinite integral, if they exist. If they do not exist say DNE: os'…

A: given,      ∫012+5xdx

Q: Evaluate the integral. -0.8 (x -208) da

A:

Q: Given ∫(−6x5 +5x3 +1)dx, evaluate the indefinite integral. Do not include +C in your answer.

A: To calculate the indefinite integral of the expression -6x5+5x3+1. To integrate the provided…

Q: Find the indefinite integral. 5 – ex e4x xp

A: the given integral is I = ∫5-exe4xdx

Q: Evaluate the definite integral: – 1| dæ

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Q: Use substitution techniques and a table of integrals to find the indefinite integral. न et (4+ e*)…

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Q: Find the following indefinite integrals Vu+u du

A:

Q: Evaluate and simplify the following integral: e* + e²x -dx 1+e2x

A: Solution: The objective is to find the value of the given integral

Q: 3lnx² -dx

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Evaluate the indefinite integral: Зд? + 3х — 5) dx +

A: We need to evaluate the following integral ∫3x2+3x-5dx Formula Used : ∫xndx = xn+1n+1+C

Q: a) [3 VIn xdx

A:

Q: Evaluate the indefinite integral: (2a – 9a? +5) dx = %3D

A: Given,            ∫2x3-9x2+5dx

Q: Evaluate the indefinite integral. -1 x2 = xp 21 (x²–7)5/2 (x² – 7) * Remember to use capital C.

A:

Q: Find the following indefinite integral. Savx2 +5 dx

A: To evaluate the integral

Q: Evaluate the indefinite integral: (7а? + 4x – 5) dæ

A: Given the indefinite integral I=∫7x2+4x−5dx

Q: Use a table of integrals or other techniques to solve the following indefinite integral. xp: x -64

A:

Q: Evaluate the indefinite integral. | #(2? + 5)* da 4

A: Given, ∫x(x2+5)4dx Substitute   u=x2+5 ⇒du=2x dx ⇒x dx=du2 ⇒∫u4du2 We know that, ∫a.f(x) dx=a.∫f(x)…

Q: t12x +9 dp

A:

Q: Find the indefinite integral. 2x (?+6) xp

A: We need to find the integral ∫2x(x2+6)5dx

Q: хра (q

A:

Q: Evaluate the integral. 9. x² + 81 dx Jo

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Q: Evaulte the integral when x > 0 ln(x^2+17x+70)

A: Integrand, I = ln(x2+17x+70)x2+17x+70 can be factorised as shown below:x2+17x+70 = x2+10x + 7x+70 =…

Q: Find the following indefinite integrals Vu + u3 du

A:

Q: Evaluate the definite integral xp, a) S b) S

A: ∫011+7x3 dx Consider, ∫1+7x3 dx=∫1+7x13 dx=1+7x13+113+17+C     ∵∫xn dx=xn+1n+1+C & x-coefficient…

Q: Evaluate the indefinite integral: ∫(x^4)sec^2((8x^5)+3)dx  HInt: Add C to your answer.

A:

Q: evaluate

A: Given- ∫π6π32sec2(w)-8csc(w)cot(w)dw We have to evaluate the given integral. Here we will  use the…

Q: Find the following indefinite integral. JaVx+5 dx

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Q: 69° (24° – 1) da

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Q: 1 (2+ √y)

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Q: Evaluate the indefinite integral x4 + 4 + C

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Q: Evaluate the following indefinite integral. xp

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Q: x'-6x+9 3. S

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Q: 3) Find each integral by substitution 2x+1

A: Given, ∫12x+1dx  we have to solve given integral by subsititution method

Q: to

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.