Evaluate the integral. 14 sin (x) cos"(x) dx Step 1 14 sin (x) cos"(x) de has an odd power of of cos(x), we will convert all but one power to sines. Since We know that cos (x) = | 1 - sin (x). Step 2 Making this substitution using | 14 sin"(x) cos"(x) dx gives us 14 sin (x) (1 - sin* (x)) cos(x) dx = 14 sin (x) cos(x) dx - dx.

Q: 100 Using integration by parts, we can convert the integral / x sin x dx to which of the following?…

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Q: Refer to the given below. Find the indefinite integral. Simplify your final answers (Just like how…

A: i)∫(2x3+12x2-5)dx=∫2x3dx+∫12x2dx-∫5dx                                   =2∫x3dx+12∫x2dx-5∫dx…

Q: (i) Use the chain rule to show that -3x = (In 3)32 dx Hint: use the fact that 3 = eln 3ª (ii) Use…

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Q: What number a>0 makes it that the area under the function f(x)=sin(2x) between x=0 and x=a is 1

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Q: Step 2 sin 6x, as used in the previous To find the integral x cos 6x dx by the parts formula, use u…

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Q: I sin³x 5 sin x 4 cos x dx

A: To find out the integration.

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Q: /4 18. sec (0) tan (0) do

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Q: Integration of Algebraic Functions By trigonometric Substitution dx 6. S x²√4-x² dx 7. S- √81+x² X…

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Q: Evaluate the integral.   7 1    (ln(x))2  / x3 dx

A: The given integral is, ∫17lnx2x3dx

Q: Find the indefinite integral. sin 70 V cos 70 de Step 1 To solve the integral | sin 70 Vcos 70 de,…

A: The given integral is sin3(7 theta)√(cos(7 theta).

Q: B. EVALUATE EACH INDEFINITE OR DEFINITE INTEGRAL. DO NOT SIMPLIFY YOUR RESULT. 21. [(12x- sec (x)dx…

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Q: 5 sinz estion 4 (The Substitution Method for Definite Integrals). Calculate dr. (3+2 cos r)?

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Q: A. First, rewrite the integral by multiplying out the integrand: | 3x° (x* + 1) dx = dx Then…

A: The given integral,         ∫3x3x4+1dx

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A: Let's find.

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Q: Consider the indefinite integral tan 0 In(7 cos 0) do For the following type theta for 0 This can be…

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Q: Find the indefinite integral. ( use C for the constant of integration) Sin(9x) cos(9x) dx

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Q: Find the indefinite integral by making the substitution x =sin e (Note: 0, "theta", represents an…

A: Answer is mentioned below

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A: Given,            ∫19-x232dx

Q: Find the indefinite integral.

A: Given,∫2sinxcosxdxwe need to find the indefinite integral

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Q: 10. S(tan x – 1)²dx

A: Topic:- application of integration

Q: Long Division (followed by Rule 17) Thursday, August 19, 2021 12:43 PM Now that you have completed…

A: Topic:- calculus

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Q: Find the indefinite integral…

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Q: How to find the antiderivative Integral 13x cos (-3x + 1) dx

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Q: Find the indefinite integral. S Step 1 / sin sin³ 70 √ cos 70 de To solve the integral Therefore,…

A: Solution

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A: Explanation of the answer is as follows

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Q: Find the indefinite integral ∫ 2sin x cos x dx

A: The given integral is ∫2sin(x)cos(x)dx

Q: 13) Calculate definite integral. Give answer as a fraction in lowest terms (x2 – 2x-3 + 3)dx

A: We will use integration rules

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Q: 1. Evaluate the integral using the Table of Integrals on Reference Pages 6 – 10. Sx'sin"(x*)&x (…

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Q: Match the integral expression on the left to an equal expression on the right. Prompts Submitted…

A: 1. =∫2sin(3x) sin(4x) 2 dx=∫12-cos3x+4x+cos(3x-4x) dx=∫12-cos7x+cosx dx=∫12[cos(x)-cos(7x)] dx

Q: Use a change of variables or the table to evaluate the following indefinite integral. |- (cos 7x-7…

A: The solution is given below:

Q: Evaluate the indefinite integral. Select the correct answer. X 64 64 cos(8x) + 64 cos (8 x) + cos(8…

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Q: 1 x² cos x dx < Use the properties of integrals to verify the inequality:

A: To use the properties of integral to verify the inequality ∫01x2cosx dx≤13

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Q: Find the indefinite integrals. 1. ∫ (8 - (1/x4))2 (1/x5) dx

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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.