(a) Evaluate the integral t tanx dx by using the reduction formula of tangent function.

Q: Find th epwation of the tangent line to An- (x-2y): 2xy-1 at print (1, 2) d [sin- (x-2g)] = (2xy-1)…

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Q: Find the equation of the tangent line to the graph of f(x) = 9 sin(x) + 4 cos(x) at x = in in the…

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Q: The slope of the tangent line to the curve at the point where x = O +1 -1 DNE f(x) = sin² x cos²x

A: The slope of the tangent line to the curve  y = f(x) at the point x= k is f '(k)

Q: 2. Evaluate the integral / sin'at dt

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Q: Evaluate the integral. ∫Sin-1 x dx

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Q: Evaluate the definite integral.

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Q: Find the equation of tangent at x = In 5: ln 2x a) y = ²x + 1 e to :

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: Evaluate the integral.  integral sin 9  x cos 3x dx

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Q: Evaluate the integral.  integral  (1- sinx )/ tan x  dx

A: Consider the given integration as

Q: Evaluate the integral.  integral sin 3  x cos 5x dx

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Q: Evaluate the definite integral. sec (x) tan (x) dx =

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Q: xe2X sin(e)dx 2x2

A: As per guideline we have to solve only one

Q: th of the curve y= ln(sin x) from x = 0 to x=.

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Q: Let y = (In x) tan 2. Find dy using the method of logarithmic dx %3D differentiation. Express your…

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Q: Find the trigonometric integral ∫ tan2 x /sec3 x   dx

A: We have to integrate ∫tan2xsec3xdx We will put tanx=sinxcosx and secx=1cosx Given integral can be…

Q: Evaluate the indefinite integral: ∫ x2 sin(x3 + 1) dx

A: ∫x2sinx3+1dx

Q: Use the composite trapezoidal rule with the step length h = 0.1 to evaluate sin x -dx, in six…

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Q: cx+ln x Determine the equation of the tangent line to the graph of f(x) cosh (V2t – 1) dt at x = 1.

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Q: Evaluate the indefinite integral. sec* (x)dx

A: We have to find the integral of sec^4(x)  Please see the explanation below

Q: Find the derivative of y with respect to x. y = In (tan -1(2x4)) dy %3D dx

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Q: Evaluate sin(x) · In ( cos(x)) dx using integration by parts.

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Q: Evaluate the integral.

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Q: ( 5tanx sec'x dx .2,

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Q: Find the indefinite integral and check the result by differentiation

A: We have to find out the indefinite integral. ∫tt2+2dt For this integral apply the substitution…

Q: (ii) Hence, by using Leibniz Rule for Differentiation Under the Integral Sign, compute the value of…

A: Leibniz Rule for Differentiation under integral sign:- ∂∂t∫atbtfx, tdx=∫atbt∂f∂tdx   + fbt, t∂bt∂t-…

Q: Find the indefinite integral. ∫arctan x dx

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Q: (a) Evaluate the indefinite integral (anti-derivative) x°(1+ 2*)® dx by using the substitution u =…

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Q: Evaluate the indefinite integral.

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Q: Evaluate the integral (exact value). e3x sin(10x) dx = %3D

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Q: the equation of the tangent line to the graph of f(x) = 9 sin(x) + 4 cos(x) at x = in the form y =…

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Q: Evaluate the indefinite integral.   ∫x Sin( x2) dx

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Q: Evaluate the integral (exact value). e3x sin(6x) dx %3D

A: Integration By Parts Formula

Q: Evaluate the integral.  integral sin 6  x cos 5x dx

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Q: evaluate the integral

A: Evaluate the integral by substitution method.

Q: Solve the Indefinite Integral. S sin Vædz

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Q: Calculate the integral (sec(x)+ tan(x))² dx.

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Q: Find the trigonometric integral ∫sin x cos4 x dx

A: Consider the integrals: ∫sinx·cos4xdx…

Q: Solve the definite integral ro e(arcsin(x)) dx. V1 - x2

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Q: Evaluate the integral.

A: Let the given integral be y - y = ∫sin-1x2dx            ...............(1)Let,x = sinθ…

Q: Find the trigonometric integral ∫sin2 x cos3 x dx

A: We have to find the trigonometric integral: ∫sin2 x cos3 x dx Rewriting the integral, ∫sin2 x cos3 x…

Q: The slope of the tangent line to the graph of y = ln x at x = a E R approaches infinity as a → 0+.

A: Given curve: y=ln x

Q: Find the indefinite integral. ∫sec x tan x/ (sec x − 1) dx

A: Given:∫secx tanxsecx-1 dx

Q: Find the indefinite integral. tan“ X dx sec x

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Q: Evaluate the definite integral.

A: ∫012arccosx1-x2 dx Consider, ∫arccosx1-x2 dx Now put, arccosx=t⇒-11-x2=dtdx⇒11-x2 dx=-dt Therefore,…

Q: Find the general indefinite integral.

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Q: Consider the implicit function. ev = sin (2x) dy in terms of x. dx Determine the formula for dy dx

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Q: sin 2x dx

A: Given the integral

Q: Evaluate the indefinite integral 1 sec (x) tan(x) dx +C

A: Given,