Evaluate the integral using the FTC I.

Q: Evaluate the integral by interpreting it in terms of areas, L(2x – 1).

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Q: Evaluate the integral by interpreting it in terms of areas. (1 - x) dx

A: We know that the area of right angle triangle is :  A = (1/2) × base × perpendicular

Q: Evaluate the integral using FTC I.

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Q: Evaluate the integral using FTC I.

A: Given integral is: int03 e1-6t dt We have to evaluate the above integral.

Q: Use a Table of Integrals to evaluate the integral. Je* sin(5z)dr + C

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Q: Evaluate the integral using FTC I.

A: Definite integral is used to obtain the exact area under a curve bounded by the intervals. According…

Q: cosa drdy =?

A:

Q: Evaluate the integral by interpreting it in terms of areas.

A: We graph the function y=|x| from x=-1 to x=2

Q: Evaluate the integral using FTC I.

A: Our Aim is to integrate the following expression given below:-∫092 dx-(i)

Q: Evaluate the integral using FTC I.

A: The given integral is ∫-32 u2 du. It is known that ∫ u2 du =u33+C.

Q: Evaluate the integral using FTC I.

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Q: evaluate the integral.

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Q: 4x sec 2x dx

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Q: Evaluate the integral using FTC I.

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Q: Evaluate the integral: In a da

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Q: Consider the integral dr

A: Given integral is: I=∫7x-3x+10dx Let us consider, u=x+10 Then we get, u2=x+10x=u2-10dx=2udu

Q: Evaluate the integral using FTC I.

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Q: Find the integral ∫(sec2ti+lntj)dt.

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Q: Evaluate the integral by interpreting it in terms of areas. /1 – x² dx

A: The given integral is as follows- I=∫-101-x2dx The given integral is a graph of quarter circle with…

Q: Evaluate the iterated integral. (a)

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Q: / In(1+ Væ)

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Q: Evaluate the integral by interpreting it in terms of area. |3x - 5 dx. Include a sketch.

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Q: Evaluate the integrals

A: To evaluate given integral.

Q: Evaluate the integral * cosh? dx -In 2

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Q: dx

A: Consider the integral  ∫022x−2dx

Q: Evaluate the integral using FTC I.

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Q: Evaluate the integral by interpreting it in terms of areas. |x| dx

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Q: Determine the integral by interpreting it in terms of areas. 2x

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Q: Use a trig substitution to evaluate the following integral:

A: We have to use trigonometric substitution.

Q: Evaluate the integral by interpreting it in terms of areas. 4 + V 81 x2) dx

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Q: Use any method to evaluate the integral. cot 2x xp- sec 2x

A: Here in this question given that a integral problem .  We use the integration formula and help some…

Q: Evaluate the integral by interpreting it in terms of areas: xp |xJ

A: The given integral is ∫-22xdx. The limit of x lies between -2 and 2. The integrand is the function…

Q: Evaluate the integral using FTC I.

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Q: Evaluate the integral cot Xdx

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Q: Evaluate the integral using FTC I.

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Q: Evaluate the integral by interpreting it in terms of areas. 2 + V 81 – x² ) dx 6-

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Q: Evaluate the integral using FTC I.

A: ∫abfxdx=Fb-Fa    F'x=fxGiven integral∫0212x5+3x2-4xdx=12x5+15+1+3x2+12+1-4x1+11+102…

Q: Evaluate the integral by interpreting it in terms of areas. (10 – 5x) dx

A: Explained below

Q: Evaluate the integral. a sec (4x) da =

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Q: Evaluate the integral by interpreting it in terms of areas. V 25 - x2 ) dx

A: Given that, The integration is the following, I = ∫-50(4+25-x2)dx We have to find the value of this…

Q: Evaluate the integral by interpreting it in terms of areas: (6 – 4x) dx =

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Q: Evaluate the integral by interpreting it in terms of areas. *18 |x - 9| dx

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Q: Evaluate the integrals ∫ tan5 θ sec4 θ dθ

A: Given information: ∫tan5θsec4θdθ

Q: Determine the integral by making an appropriate substitution. et6

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Q: Evaluate the integral using substitution as an aid: x (2x* + 1)2dx

A: Consider the integral

Q: 23x xp

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Q: Evaluate the integrals ∫et√(tan2 et + 1) dt

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Q: Evaluate the integral using FTC I.

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Q: Evaluate the integral using FTC I.

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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.