Evaluate the definite integral S, x°dx. Afterward, sketch a graph of y = x³ and use it to give a geometric interpretation of the result.

Q: The definite integral f(r) dr can be interpreted as

A: Given: The definite integral  can be interpreted as

Q: Evaluate the following integrals. (a) / (sin æ)(tan²r + csc², x) dx

A: As per our guidelines we are supposed to answer only ? 3 sub- parts ( if there are multiple sub-…

Q: Find the Definite Integral Exactly and use Desmos to explain what you just found. -2 3. S²(x² - 3*)…

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Q: Evaluate the definite integral. Write your answer in terms of . (y +1) dy

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Q: Approximate the definite integral "by hand," using the Trapezoidal Rule with n =4 trapezoids. Round…

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Q: Find the value of the following integral: * COS2 dx,a>0

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Q: Evaluate the definite integrals using the graph of f (æ) below. 4- y 2- 2 10 12 co to 4. 2.

A: ʃab f(x) dx = Area under the curve f(x) between a to b.

Q: In the following given equations , decide whether the integral is improper. Explain your reasoning?…

A: ∫0∞ cosx dx

Q: Determine the following definite integrals: (a) (sin(x) + =) d.x

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: d) V1+x? dx

A: Consider the provided question, We need to evaluate the definite integral ∫01 x31+x2dx

Q: (b) [* x'sin (x) dx

A:

Q: The integral S₁ substitution is used? dx (x²+4)² can be transformed to which of the following when…

A: Let's integrate by using trigonometric substitution.

Q: Use a graphing calculator to evaluate the integral 2 e dx.

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Q: Evaluate the definite integral. Si f (x) dæ, f (x) =4"-(7a+ 13)/a?

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Q: Evaluate the integral. | æ sin(9r) dæ + C

A: Given,  ∫  x sin(9x)dx

Q: If f(x) has units of "pounds per foot" and x is measured in feet, what are the units of the integral…

A: Given, fx has a units of "pounds per foot" and x is measured in feet . We have to find the units of…

Q: Determine a definite integral that represents the area of the petal that points to the right from…

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Q: * Which of the following integrals will yield an inverse trigonometric function? ydy A 25+y2 B) none…

A: In option (A), If we substitute 25+y2=t2⇒ydy=tdt, then the numerator will be replaced by tdt and…

Q: Evaluate the definite integral.

A: Given: I=∫oaxx2+a2dx          , a>0 for evaluating given integral, we substitute x2+a2=t2…

Q: For the definite integral, do the following. Vx2 - 16 dx (a) Evaluate it using the table of…

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Q: Evaluate the following definite integrals arcsin x (a) L 1. V5 + 4x dx (b) dx V1 - x2

A: We have to solve the definite integral

Q: Evaluate the definite integral ,x°dx. Afterward, sketch a graph of y = x³ and use it to give a…

A: Given,  ∫-21x3dx  We have to evaluate the definite integral and sketch  a graph of  y = x3 to give…

Q: Evaluate the definite integral: - 6 e!/I dx

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Q: Use the properties of the definite integral to find -g(x)dx, if possible, given that g(x)dx = - 7.…

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Q: -2 2 [ 7e +- y -5

A: solution:-∫-5-27ey+2ydy=∫-5-27eydy+∫-5-22ydy=7∫-5-2eydy+2∫-5-21ydy

Q: Find the following integral. | tan? x sec* x dx

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Q: use the Change of Variables Formula to evaluate the definite integral.

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Q: dx c1 16. 21 1)

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Q: Use the graph to evaluate the following integrals: Use pi to represent t h(x) dx =

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Q: f (x) dx 5- 10 -5-

A: Negative

Q: evaluate the following definite integrals : a) tan? * dx

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Q: 2 dx 2 4 + x?

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Q: Use this figure to find the following definite integrals:

A: The figure given in the problem represents the graph of the function y=f(x). The region under the…

Q: Find the following definite integrals. sin a dr

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Q: 3 E (It=X) xp x te

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Q: If you are going to evaluate the integral f dx using trigonometric substitution, the answer is 2(tan…

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Q: Evaluate the indefinite integral. tan? x dx Answer: + C

A: We have to find ∫tan2x dx

Q: Evaluate the definite integral. c (x) tan (x) dx = se 0.

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Q: | sec* x tan x dx

A: Given integral is ∫π4π2sec4x tanx dx

Q: Find the value of the following integral: cos2r dx,a>0 71+a

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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 following integrals. When using substitutions, be show to show them explicitly. a) + 5…

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Q: evaluate the following definite integrals : a) tan? X dx

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Q: Evaluate the definite integral: = rp |I – ,7|

A: Given: I=∫05x2-1dx   From the rule of inequality; x2-1<0 when -1<x<1x2-1>0 when x>1…

Q: Evaluate the definite integral. t10 sin (t11) dt

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Q: Which expression represents the midpoint approximation M3 to the integral r12 sin (/æ) dx?

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Q: [sin x dx

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Q: Use the substitution x = 6 sec t to evaluate the integral f dx xvx²-36 Note: Use C for an arbitrary…

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Q: Write the integral as the sum of the integral of an odd function and the integral of an even…

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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.