Using suitable method, show that 2 tan" (x+2) dx =- – In 2 .

Q: Find the indefinite integral ∫sin 5x sin 4x dx

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Q: ( tan (sin-1x)+sec*(sin¬1x) V1-x? dx

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Q: 5- (tanx + secx)2 dx

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Q: Differentiate. y = In Sin x  - 1/2Sin2 x

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Q: 2cos^2(?) sin3? dx

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Q: 5. tan (x)dx 1 -dx cos² (x) sin () 6.

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Q: Evaluate

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Q: 4 f sin(5 – 6x) sin (6x – 4)dx -

A: Here limit are not given so we integrate only without using of limit.

Q: csc squared x/2 = 2/1-cosx verify with steps

A: To Verify:

Q: Find y' i. y = sin(2x² + tan(6x² – x)) ii. y = sin(2x² + tan(x – 1))

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Q: Evaluate the integrals

A: We have to evaluate the integral;  13) ∫ln4ln9ex/2 dx14) ∫tanxln(cosx) dx

Q: 7/3 x tan (x) dx 2

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Q: Integral from 0 to 2pi of sin(2x) dx

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Q: Find the indefinite integral ∫ 3√(tan x) sec2 x dx

A: ∫tanx3sec2x dx Now put tanx=t⇒sec2x=dtdx⇒sec2x  dx=dt

Q: find integral tan 3 x dx

A: To find the integral of tan2x first split tan into two part and the using property of sec and tan…

Q: 3- Sin4x dx S 3-Sin4x dx ノo

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Q: Find integral.

A: We have to find the integral: ∫tan 7x dx We know the integration formula, ∫tan x dx=lnsec x+C∫tan ax…

Q: Find integral.

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Q: Using secant method, detemine a root of sin Vx - x with initial guesses xo = 0.5 and x, = 1…

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Q: Integral from 0 to pi/2 of (cosx) /(sinx) ^(1/2) dx

A: we have to find definite integral of f(x) in [0,pi/2]

Q: 16. Using the Quotient tanx= sinx/cosx to prove d/dx tanx=sec2x

A: Quotient rule of differentiation

Q: 5sin(4x + )sin(2x-)dx

A: The given integral is, The integral cannot be solved directly and we would have to use some…

Q: elin (sin x+ cos x) dx 1. S ecosx

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

Q: ( sin (In 2x) - cos (in 2x))? +x dx 2x

A: Let's find.

Q: Find the indefinite integral

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Q: Find sine half range for f(x) = \cos x for -1<x<1 COSX for < x < 0. f(x) { COSX for 0 < x < .

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Q: integral sec2(?) tan2(?) d?

A: Given that sec2?tan2?d?To find : Integral Solution :∫sec2?tan2?d?Let, tan?=tsec2?d?=dt∫t2dtt33+c

Q: (ii) Show that 1 d (tanh-1 x) = dx 1- x2 Hence, or otherwise, show that, 27 tanh-1x dx =- In 4 2. 1…

A: Evaluate: and

Q: lim (x approaches 0) of [sin(5x)cos(6x)]/(x)

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Q: Find the indefinite integral ∫sec2 (x/2) tan (x/2) dx

A: Given: I=∫sec2x2tanx2dx

Q: integral of sin2x.cos2x dx

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Q: ∫√1 - sin^2 x dx

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Q: (B) Evaluate tan (3.x +1) sec³(3x +1) dx

A: In this, We find the value of the given integral using tan^x+1=(sec^2)x formula.

Q: Integral of tan^4(x)sec^6(x)dx

A: Sincesec2x=1+tan2xTherefore,

Q: 1-sin x dx 1-cos x 2

A: Introduction :

Q: Si cos°(3x)sin (3x) – cos (3x) sin°(3x) dx

A: First we common out cos7(3x) sin7(3x) and then apply the formula cos2(3x)-sin2(3x)=cos(6x)

Q: eCoS ecos x sin x dx In x 2. Vx 3. tan'x dx

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Q: 2cosx dx 5- f 1+(sinx)2 a)2 tan sinx| b) 2 In sinx| c)2 In(1+ (sinx)1

A: We use Trigonometry substitution method

Q: Ssec*x (Vtan²x + 1) 2. 4 sec' x tan3, dx

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Q: 3. sin 8x cos 8x dx s 2x sin 2x dx cos

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Q: 2cosx dx 5- ? 2 1+(sinx)2

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Q: What is the antiderivative of  2(sin(2x))/sin(x)?

A: The anti-derivative of a function is a differentiable function whose derivative is equal to the…

Q: Use integration by parts to verify the reduction formula.

A: We have to verify the reduction formula using integration by parts: ∫sinn x dx=-sinn-1 x cos…

Q: Integral of tan^5(x) dx Show Complete solution

A: This is a problem of differentiation. By general formula we will solve the question. Assume, secx =…

Q: dx 2 sin x - cOS X |tan+ 2 + V5| In 5 tan; + 2– V5 |tan+2-V5 + C + 2+ V5 2. + C In Option 1 O Option…

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Q: cosh(In x) dx

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Q: Find sine half range for f(x) = \cos x for -t< a <n %3D cosx for f(x) for 0<x <n. cosx

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Q: Use integration by parts to evaluate (tan- dx. Express your answer in four (4) 2 decimal places.

A: By part integration: integration uv = u(integration v) - integration ( (u')(integration v))

Q: Cos x dx In x (sin x) () - dæ. (In x)²

A: We have to find the value of the integral : ∫cos(x)ln(x)dx-∫sin(x)1xln(x)2dx

Q: Find y' i.y = sin(2x² + tan(6x² – x)) ii.y = sin(2x² + tan(x – 1))

A: We have to differentiate the given functions

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.