Find the indefinite integral and check the result by differentiation. dx 9x2 Part 1 of 7 Observe that-18x is the derivative of (5 - 9x?). Let g(x) = (5 – 9x2). %3D -18x Multiply and divide the integrand by -18 -18 and rewrite the integral. 1 -3 9x2 dx = - 18 / (5 - 9x²)°(-18x) dx 18 Part 2 of 7 (s - 2²) * -3 | -3 9x2 Now, g'(x) = Define f(g(x)) : such that f(x) = %3D -18 -18 Rewrite the given integral in terms of g(x). 1 -3 dx = 9x2 (-18x) dx 5 - 5 – 9x2 - Ja f( (x))g'(x) dx %D »] + c F(g( f(g(x))g'(x) dx = F(g(x)) + C %3D where F(g(x)) is the antiderivative of f(g(x)).

Q: Given the integral ( 12x3 + 7 dx -5 Use the integral table to help you find the Anti Derivative of…

A: To evaluate: ∫-5712x3+7 dx We know that  ∫xndx=xn+1n+1, ∫kf(x)dx=k∫f(x)dx and  ∫abf(x)dx=F(b)-F(a),…

Q: What is the derivative of y= 3Arcsin xº, 3 Arcsin x In 3 A y' = 1 - xa 3 Arcsin x* In 3 3 B y' : (а…

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Q: Find d2y/dx2 by implicit differentiation x3 + y3 = 1

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Q: Can you help me with this problem step by step?

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Q: Q2/ A/ Show that the functions f(x) = sin-1() and g(x) = 2tan-Vx, have the same derivative. %3D

A: Given : f(x)= sin-1 ( x-1 / x+1 ) g(x) = 2 tan-1 (√x)

Q: d 5x+3 4. dx 7x+2

A: As we know that; The Power law: ddxxn=nxn-1 The Quotient rule: fg'=f'·g-g'·fg2 And c·f'=c·f' ; where…

Q: Find the derivative of the follo solutions. 1. What is (5x +3)4? dx 2. What is 4 (x2 – 3x)5? dx 3.…

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

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

A: Given: Let I=∫x21+x32 dx To Find: To evaluate the given integral and to check the result by…

Q: -4t Find the indefinite integral dt and verify the result by differentiation. (t2+3)3

A: Integrate using substitution than take derivative to verify the result.

Q: 6. y = (x +3x + 2)(x2 +5x + 1)

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Q: Compute the higher derivative.

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Q: 2 Suppose that x and y are related by the equation 4x² - 3y² = 5 and use implicit differentiation to…

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Q: d,x+7 3. dx 2x-3

A: To find: ddxx+72x-3

Q: Find one anti derivative of (x+1)^2 and then find  integral(x+1)^2 dx.

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Q: Q8/ Use implicit differentiation to find of the following curve at the point (2, 3). dx2 2x3 – 3y2 =…

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Q: Q2) Apply the differentiation rules to find the derivatives of: Inx 5 (a) y=x*.e*+2- Inx- cosx (b)…

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Q: a)  Use the hyperbolic identity sech^2(x)  = 1 - tanh^2(x)  to solve 4tanh^2 (x)  + sech^2(x)  =3…

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Q: Verify the formulas by differentiation. ∫1/(x + 1)2 dx = -1/x + 1 + C

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A: the given expressions is: dex-e-xex-e-xdx the given function is: f(x)=ln2x+133x-14

Q: 11) Гx + 7)dx

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Q: (3e)® arctan (3x³) In(e2«) arccos(5x) 1. Find the derivative of f (x)

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Q: a) Use the method of Differentiation from first principle to prove that the derivative of the square…

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Q: 6. Find the derivative of function. a) y = (x - 1)ā + 2x2-4x+7 b) y = cos* 3x * arcsin 3x2 |3D 3 c)…

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Q: x2 1)Calculate the derivative using FTC(1): g(x) = ʃ  (t5 − 9t3 )dt…

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Q: Find the first derivative of the following: 1. y= y = Ine-tanh² 2x 2. Y= sech(5x-1)tanh(5x-1) 3.…

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Q: -1/7 17 dx =?

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Q: Find the derivative of the function using implicit differentiation.  1.) x²y + y²x = -2  2.) √(xy)…

A: 1.) x²y + y²x = -2    2.) √(xy) = x²y+1 ntiderivatives for integral notation. (x+7) dx

Q: Find the value of the definite integral: 4x dx -2

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Q: 4 %3D ») f(E) =

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Q: 4 sin x-3 2. Find the first derivative of y =150xcos (10x)+ 9 In(J16-x)

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Q: Find the indefinite integral and check the result by differentiation                   ∫(x2 −…

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Q: x3+6x-2 dx x4+6x2

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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: Evaluate the integral. sinh 5a -dx +C. 5x

A: Evaluate the integral the given function Sinh is hyperbole function.

Q: (a) Show that the derivative solution of this function y = x** is x(x*+x-1) [1+x In x (In x + 1)] dx

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Q: dy/dx for (ln(tan(2x)-sqrt(3+e^2x) / (pi(x)^3-cos^2(-5x))

A: Given,     y  =  ln(tan2x)-3+e2xπx3-cos2(-5x)

Q: Determine the derivative of y=tan(cos-'(4x)) -1 A y'= 4x2/1- 16x2 - 4x B y'= V1- 16x2 c) None of the…

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Q: 10.Suppose that x and y are related by the equation 5x 2−4y 2=2 and use implicit differentiation…

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Q: 8. (a) Evaluate the indefinite integral dx sinhx+coshx e 4x (b) Find and simplify the derivative of…

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Q: 1. Find by implicit differentiation for xe = 2xy + y³.

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Q: 5. Find by implicit differentiation for x + y = xy. dx

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Q: Suppose x6 e-5y = In (xy). Find Y by implicit differentiation. 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.