Let the domain of the function f(x) = log4 (log, (log3(18x – x² – 77))) be (a, b). Then the value of the | - integral J Tsin°+sin*(a+ba) sin3x 3 dx is equal to

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: A linear differential operator g D is called    annihilates the functions fx if and only if…

Q: Solve: The indefinite integral of the integrand (cos x/1+sin2 x) dx

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Q: Find the indefinite integral. ∫cos3 x sin4 x dx

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

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

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Q: Find the definite integral.

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Q: Evaluate the definite integral. sin x dx -dx J12 I+cos² x

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Q: Evaluate the indefinite integral. [ (sin-æ)3 dx : +C. V1 - x2

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Q: Evaluate the definite integral (if it exists) 1/3 -4 sin(x) dz cos² (1) If the integral does not…

A: Substitute cos(x)=t⇒-sin(x)dx=dt At x = 0, t = 1 At x=π3, t=12 The definite integral is: I=4∫112dtt2

Q: find a linearization at a suitably chosen integernear a at which the given function and its…

A: fx=sin-1x,   a=π12 The value of the function and the value of the derivative can be easily…

Q: Find the indefinite integral. X cos 8TX2 dx

A: To evaluate the integral: I=∫x cos 8πx2 dx⇒I=∫cos 8πx2 x dx...(1)

Q: Show that In(x") = y In(x) for all x, y > 0, only using the rules of derivative for the natural…

A:

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

A: ∫x2sinx3+1dx

Q: Find the indefinite integral. ∫(x2 cos x)dx

A: The given integral is ∫x2cosx  dx. Let u=x2  and   dv=cosx dx. This implies that du=2xdx  and…

Q: Find the indefinite integral

A: To find the indefinite integral: ∫sinx7+cos2x dx Solution: Let substitute t=cosx Differentiating…

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: Evaluate the definite integral. sec (x/4) dx 0.

A:

Q: Find the indefinite integral. | x cos 9x² dx

A: Given : ∫xcos(9πx2)dx

Q: Evaluate the integral ∫(sin-1(x/5))2/√(25-x2) dx

A: NOTE: Refresh your page if you can't see any equations. . ...............(1)

Q: Evaluate the integral.

A:

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: Find the indefinite integral S (8x2/3 + 5* – cos(x))dx and verify the result by differentiation.

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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: 7. To evaluate f-cos X-1 dx, the integrand can be transformed to? 1-sin? x

A: Follow the procedure given below.

Q: Find the definite integral from 1 to 3 of |-3x+1| dx

A: According to the given information it is required to find the value of the definite integral.

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

A:

Q: Find the indefinite integral ∫ cos2 x sin4 x dx

A: Given: I=∫cos2xsin4xdx we know that ∫sinnxdx=n-1n∫sinn-2xdx-cosxsinn-1xn                   ..1

Q: 6) S(x + 2)dx

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

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Q: cos (x)sin(x)dx

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Q: Evaluate the indefinite integral: cos° x sin x dx

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: See the detailed solution below.

Q: Evaluate the definite integral. 1 2 sin-'(x) dx /1 – x²

A:

Q: In the function:  f(x)= (3x^2)ln(x) , x>0 Where is the function increasing and decreasing in…

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

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Q: 3. Use Log Rule to integrate. J6x-5 dx a. 6х-5 b. S- 1 dx x Inx

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Q: Find the definite integral of sin x -dx 0 1+cos x

A: Given: I=∫0π2sin x1+cos xdx

Q: 4. Compute the derivative of f(x) in each part. (a) f(x) = sin(ev) (b) f(x) = (tan r)", x € (0, 7/2)…

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Q: Evaluate the integral. 2 sin -1 x dx

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Q: Find the interval in which function f(x) =sin (logex)+cos(logex) is decreasing

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Q: (sin-l x)² dx V1-x²

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: Use U-Substitution to evaluate the definite integrals. Sž cos 2x dx (1+x2)2

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Q: Find the indefinite integral  ∫sin3 x cos2 x dx

A: We have to find the indefinite integral ∫sin3 x cos2 x dx

Q: Evaluate integral 0 to pie sin 2 x cos 3 x dx

A: Explanation: Given that,  ∫0πsin2xcos3xdx   Formula Used: Trig. identity:1-sin2x=cos2xSum rule of…

Q: Evaluate the definite integral. 1. 2 cos-¹(x) √1-x² dx

A: Given Problem:- ∫-11-2cos-1x1-x2dx

Q: arc sin z = -i log(iz + V1- 22).

A:

Q: How many integers are there in the domain of the function f(x) = ln (x² – x – 12) + v25 – x² +…

A: The domain of a function is the set of input or argument values for which the function is real and…

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: The given function = 10x+ 9x2-sin6x

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.