Use the identity sin? x = 1– cos²x to write f sin?x cos?x dx a sum of two integrals and then evaluate using the reduction formula.

Q: Evaluate the following integrals. Show the solution. 1. S csc? (7x + 5) dx 2. fx? sec (4x³ + 9) dx…

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Q: -It/2 S cos (x) esin (x) dx 0.

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Q: Evaluate sin x cos? x dx in two ways. First use u = sin x to show that sin x cos? x dx = [ uvT - u²…

A: Given indefinite integral is

Q: Evaluate the following integral: ( a ) |sin? xcos“ xdx 4

A: Topic - Integration

Q: Evaluate the definite integral. cos(T2) dz sin 8n Answer:

A: The given integral:∫08cosπxdxWe need to evaluate the above integral.

Q: 2rx · sin(rx²)dx sec²(/x) dx

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Q: Suggest a trigonometric substitution for each integral, and then write the new integral that results…

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Q: Use the indicated substitution to evaluate the integral. -3 cos x sin (sin x) dx , u= sin x 3 sin…

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Q: The integral of (10*/ cos 10*)dx may be written as A In sec B* + tan B*|+ C. Where A, B, and C are…

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Q: Use the substitution formula to evaluate the integral. 3 coe? x sin x dx /3 129 1024 O 21

A: From the given problem: I=∫π32π3cos2xsinxdx    ...1 Using the substitution method to find the…

Q: Evaluate the integral. 7 sin?(t) cos (t) dt

A: Evaluate the integral as follows.

Q: sin (20) cos (20)de

A: Integration of the function helps to find the required value of the given expression. Integration…

Q: .4 sec'x (V tan³x + 1 ) dx

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Evaluate the Integral.

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Q: Use an appropriate substitution and then a trigonometric substitution to evaluate the integral. dx…

A: We have to find the integral

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

A: Given,  ∫  x sin(9x)dx

Q: #2

A: To find out the integration.

Q: The given integral (cos?r – sin²x) dx is equal to

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Q: 10 Sin h (Ux)

A: we have to find integration

Q: (i)[ cos (5x) sin 5.x dx

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Q: The integral of (10*/ cos 10*)dx may be written as A In | sec B* + tan B* | + C. Where A, B, and C…

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Q: Evaluate the integral. | (sin? 0 + cos? 0)d0 е — т те т — е 2т3

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Q: Use a computer algebra system to find or evaluate the integral.

A: Given :           The integral function :                   ∫-π4π4 sin2x - cos2xcos x dx

Q: indicated

A: We have to calculate the indefinite integral using the given information

Q: Using substitution with u= sin(2x), the definite integral | 4 sin³(2x)cos(2x)dx is equivalent to (A…

A: The given integral is ∫0π4sin32xcos2xdx.

Q: Evaluate the following integral and show your work: sin? x · cos? xdx ,2

A: Given :            ∫ sin2x cos2x dx

Q: Use the given substitution to evaluate the integral.

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Q: 2 sin? t sec“ t dt

A: To determine:

Q: 2 sin e r cos? 0 dr de

A: The integral is evaluation is explained below.

Q: Evaluate the integral si 3. sin° x adx. cos? 2

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Q: Use the given substitution to evaluate the integral

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Q: evaluate using Integration by Parts, substitution, or both if necessary.

A: Given integral is By using the following substitution, we get

Q: 0. sin? x cos? x dx

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Q: 6 ∞ 9 cos (7) x² dx I

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Q: Evaluate the integral and check your answer by differentiating. sec(x) + cos(x) dx 9 cos(x) + C

A: Formula : ∫sec2x=tanx+c

Q: use the indicated substitution to evaluate the integral.

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Q: Evaluate the following integrals.

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Q: Evaluate the following integral

A: Consider the given integral

Q: Find the definite integral of: * 27 cos -w ) sin w) dw. O - 1/2 O - 1/12 О 12 2

A: The given integral is ∫π2π cos3w2 sin5w2 dw. Evaluate the above integral as follows.

Q: Evaluate the integral. | (sin? 0 + cos? 0)d0

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Q: Evaluate the following integrals. 1/2 (b) sin? 0 cos OdO

A: Given I=∫0π2sin2θcos3(θ)dθ

Q: Evaluate the following integrals.

A: Given: The integral ∫sinxcos2x+cosxdx To evaluate: The given integral.

Q: Use the convolution theorem to evaluate the integral. sin(2 · 7) cos((t – T))dr COS

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Q: 3(cos x)²+2 -dx 2(cot x)°+4 cot x-5

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Q: Use the substitution formula to evaluate the integral. 27 3 cos2 x sin x dx 1/3

A: Given that: ∫π/32π3cos2x.sinxdx

Q: What is the integral of cos xdx from pi/3 to pi/2? A 0.134 В 0.500 C) 0.293 D) 0.707

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Q: To evaluate the integral x² dx, x² -4x + 20 using trigonometric substitution, which substitution…

A: Answer is option B.

Q: 27n 4 cos x sin x dx 7/3

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Q: If you are going to evaluate the integral f cos x v9 + 25sin-x dx using trigonometric substitution,…

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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.