The improper integral

Q: Use the substitution formula to evaluate the integral.

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Q: Vx² – 1 -dx

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Q: Use integration by parts to evaluate the integral: In(s)ds

A: Given, To Evaluate

Q: Find the integral.

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Q: Evaluate the integral using Algebraic Sub. Vax dx Vx -

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Q: dx

A: Consider the integral

Q: 16-y2 16 – 22-y drdy by using appropriate coordinate system. an

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Q: Evaluate the Improper Integral (Type 1)

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Q: Evaluate the integrals ∫2 sec3 x dx

A: To Find: The following integral Formula Used: Common Integral :

Q: integral

A: Please refer to the image below

Q: Evaluate the integrals

A: the given expression is : ∫π3πcot2x6dx

Q: Apply trapezoidal and Simpson's rules to the integral

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Q: et e* +e

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Q: Find the integral

A: To find- Find the integral ∫ex sinx dx     Concept Used-  Integration by Parts formula: ∫ u v dx = u…

Q: integral

A: We have to find the value of the given definite integral

Q: Write a definite integral that represents the area of the shaded region and compute the integral…

A: We have the given curve as y=-x+4 At y=0, we get the value of x as 0=-x+4x=4

Q: Evaluate the integral using integration by parts. sin dx

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Q: integral

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Q: Use Property 8 to estimate the value of the integral.

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Q: integral

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Q: Evaluate the integral using integration by parts. 2xe3* dx

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Q: 2x dx Vx+3

A: Topic = Integration Use∫xn dx=xn+1n+1+C

Q: Evaluate the integral. du

A: Evaluate the given integral.

Q: Identify the u, du, the form of the integral

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Q: 25 dr. valuate the integral: re

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Q: -dx

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Q: Evaluate the integral.

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Q: find the value of the improper integral

A: Given that, the integral is ∫2∞1xln2xdx To evaluate the integral  By using substitute method,

Q: Use a double integral to find the area of the specified region. 25 y = 25 - x 20 15 10

A: Use double integral

Q: evaluate the integral

A: Consider the given integral function,

Q: Evaluate the integral 1 x(110) dx Integral =

A: Given integral is,

Q: Evaluate the integral cot Xdx

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Q: Evaluate the improper integral or state that it diverges. dx

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Q: Find the area represented by the definite integral.

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Q: Evaluate the integral ex dx.

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Q: Evaluate the integrals ∫sec4 x tan2 x dx

A: Given: ∫sec4xtan2xdx

Q: \ Calculate the double integral

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Q: Evaluate the improper integral dr. /sin z

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Q: Find the integral: Ste 72 dt

A: Consider the integral is, I=∫te-7t2dt Then, consider the value of u=-7t2 then, du/dt=-14t and…

Q: Evaluate the integral using appropriate substitution ∫(x^2 +1)/(√(x^3 +3x))dx

A: Given an integral: ∫x2+1x3+3xdx Let, x3+3x=t t=x3+3xdt=3x2+3dxdt=3x2+1dxdt3=x2+1dx Substitute value…

Q: (12) Sz sec¹z dz.

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Q: the integral using the indicated trigo V-64 dr. x = 8 sec(@)

A: The answer is, C - (8/x), where, C is the constant of integration.   The detailed solution is as…

Q: Sec?(sx +8) dx=

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Q: Calculate the iterated integral.

A: First integrate wrt y then x

Q: * dr; By using Trapezoidal Rulc, calculate the integral

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Q: 3. x+1 dx

A: let I=∫5x32x+1dxput 2x+1=u2x=u-1x=(u-1)2and  2x+1=udifferentiate w.r.t.…

Q: 5. Ssin' x dx.

A: I am attaching image so that you understand each and every step.

Q: o. dr. re Evaluate the improper integral

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Q: The value of the triple integral

A: Integration is the process of finding the anti-derivative function of the given function. The…

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.