Evaluate   ∫01 (x  +  √(1 -x2)) dx   by interpreting it in terms of areas.

Q: Evaluate the definite integral. 9. (-3x + 6) dx J3

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Q: Evaluate the integral. x³ + 4 - dx (x + 4) (x + 3)

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Q: Use symmetry to evaluate the following integral. 6 | (36 -x) dx -6 | (36-x) dx: -6

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Q: Evaluate the integral. 3) S- dx x/ 16x2 - 7

A: As per the guideline we are solving only first question. Kindly repost the other question in the…

Q: Evaluate the improper intergal 1 dx using the residue (x² + 100)? theorem.

A: The given problem is to evaluate the given improper integral using the residue theorem. We have to…

Q: Evaluate the definite integral.

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Q: Evaluate the integral. X- 8 dx x2 - 7x + 10 Jo

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Q: sec²(x) √2-3tan (x) dx

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Q: Use the Midpoint Rule with n = 3 to approximate the integral 16 | (- 10x + 2x2) dx 10

A: In this question we will use basic of calculus i.e concept of midpoint rule to approximate the…

Q: Use geometry to evaluate the definite integral -2∫2 √4−x2 dx

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Q: evaluate the integral.

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Q: Evaluate the integral. | (7x2-6x +7) dx

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Q: Evaluate the definite integral. dx x/ In x 64

A: Given definite integral ,∫e64e81dxln xxNow , ∫dxln xx   Let , ln x=z2 ⇒z= ln x         =…

Q: Show that (In kx) dx (In x), where x > 0 and k is a positive dx real number.

A: ddxln kx=ddxln x, where x>0 & k is a positive real number.

Q: 9x2 - 4 dx

A: Given that, Apply u-substitution: Differentiate both sides with respect to x, Plug the values of…

Q: Evaluate the integral. dx 4 - x3

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Q: Evaluate the integral. (6x2 - 8x + 4) dx

A: Given integral is definite integral. So we first evaluate it and then we will put limit. PFA here…

Q: 4 dx = x² + 1

A: Given that, ∫-114x2+1dx=4[tan-1x]-11 =4[tan-11-tan-1-1]=4[π4-(-π4)]=4[π4+π4]=4×π2=2π

Q: Evaluate the integ ral dx x "+ 4

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Q: Evaluate the integral. dx :- X>8 x2Vx² -64 S- xp x²Vx² - 64 %3D

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Q: find integral 1/ sqrt ( x2 - a2 ) dx , where a >0

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Q: Evaluate the itegral by interpreting it in terms of areas. 0. 3 + 100 - x2 ) dx -10

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Q: 5. Evaluate x + v1 – x² dx by interpreting it in terms of areas.

A: We have to consider it as sum of two functions.

Q: Evaluate the integral

A: Given: I=∫xdxx2-7 for evaluating given integral, in given integral we substitute x2-7=t…

Q: Evaluate the integral. x³ - 6 dx +ク 11 X

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Q: evaluate the integral.

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Q: Evaluate the integral∫ (4 /√(4 - x2)dx.

A: Let, I=∫44-x2dx Substitute x=2sint  gives dx=2cost dt…

Q: dx x2-x

A: Convert the rational function into partial fraction. Use integration of 1/x dx = ln(x) +c

Q: evaluate the indefinite integral / dx. Av7² – 4 xª/x² -

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Q: Evaluate the integral 4х + 5 dx. 3 - x2

A: To find the integral

Q: (2x-1 +3x²)dx

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Q: Evaluate the integral. X - 4 dx Jo x2 - 5x + 6

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Q: Evaluate the improperruk MANUSIA dx (5 – x)3 K OKERANA TO

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Q: Use substitution to find the general integral (x-4) *dx x²(x- 4) $dx = %3D |

A: We have to find the integral

Q: Consider the indefinite integral 7x4 dx 7x5 – 9 - (a) The most appropriate substitution

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Q: evaluate using the appropriate method or combination of methods.

A: We will need by parts method with

Q: evaluate using the appropriate method or combination of methods.

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Q: evaluate the definite integral.

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Q: the sketch, Evaluate & reverse of integral 3. dj dx

A: Definition used- Reverse the order double integral – In double integral, we can reverse the order of…

Q: Evaluate the integral arcsin(x) d.x x²

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Q: Evaluate the integral f(4x³ + 5x* + 2)dx

A: ∫xn dx xn+1n+1+C ∫a dx ax + C

Q: Evaluate the integral. 9x2 +x +1 -dx

A: Solve by integration

Q: Evaluate the indefinite integral. x² A -dx 1- x6

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Q: Evaluate the integral. 2. (9x2 - 8x + 6) dx

A: the Integration is a process of finding the anti derivative of a function. There are basically two…

Q: Evaluate the integral 4x³ dx

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Q: To evaluate the integral/ V3 – 3x² dx,

A: Substitute, x=sin(θ)dx=cosθ dθ The expression f(x) becomes,

Q: Evaluate the integral /4- x2 dx. x2

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 16. Evaluate x + v1- x² dx by interpreting it in terms of areas.

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Q: 3x? V2x3 - 5 dx

A: To solve ∫133x22x3-5dx

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.