Use x2 dx = 9 to evaluate each definite integral without using the Fundamental Theorem of Calculus. (a) x² dx (b) x² dx (c) -6x² dx (d) 9x2 dx

Q: Evaluate the indefinite integral. 3x sin(4x)dx

A: The given integral,      ∫e3xsin(4x)dx

Q: In this problem, use properties of definite integrals. 9. Vx2 - x² - 1 dx. Evaluate

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

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

A: Given: Let I=∫5x 1-x23 dx To Find: To evaluate the given integration and to check the result by…

Q: sec 3x tan² 3x dx

A:

Q: Find the indefinite integral.

A: We have to solve the indefinite integral: ∫tan x3 sec2 x dx Solving the integral by substitution…

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

A: To find the integral I=∫6x24x3-93dx

Q: Find the indefinite integral and check the result by differentiation                   ∫x2(6 − x3)5…

A:

Q: Use x2 dx = 9 to evaluate each definite integral without using the Fundamental Theorem of Calculus.…

A: a) ∫-33x2dxb) ∫-30x2dxc) ∫03-6x2dx

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

A: Given, I=∫x2-932xdx

Q: Find the indefinite integral ∫tan3 3x dx

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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                   ∫√(25 − x2…

A: Now put

Q: Use the Fundamental Theorem to evaluate the definite integral exactly.   ∫83(x3−πx2)dx

A: Given:

Q: Find the indefinite integral. ∫(sec 2x + tan 2x) dx

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Q: 17. x dx

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

A:

Q: Evaluate the indefinite integral: ∫ sec2 x tan4 x dx

A: Evaluate the indefinite integral. ∫sec2xtan4xdx Let tanx=tsec2xdx=dt

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

A: |The indefinite integral ∫(4t2+3)2dt

Q: Evaluate the integral ∫tan2 x sec2 x dx

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Q: Find the indefinite integral and check the result by differentiation                    ∫ x2(2x3 −…

A: Consider the following integral: ∫x22x3-14dx Substitute 2x3-1=u→6x2dx=du→x2dx=16du in the above…

Q: Find the indefinite integral and check your result by differentiation. (Use C for the const (x³ -…

A: The given integral is ∫x3-12x-4dx use the integration formulas, ∫xndx=xn+1n+1+C∫dx=x+C use the…

Q: 4 dx = x² + 1

A: Given that, ∫-114x2+1dx=4[tan-1x]-11 =4[tan-11-tan-1-1]=4[π4-(-π4)]=4[π4+π4]=4×π2=2π

Q: Find the indefinite integral

A:

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

A: Given, I=∫x34+1dx Or  I=∫x34+1dx

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

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

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

A: Given: I=∫dx2x We know that ∫xndx=xn+1n+1+c                                                   ..1

Q: Find the indefinite integral and check the result by differentiation. ∫3√x2 dx

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Q: Find the indefinite integral and check the result by differentiation.                   ∫(x3/2 + 2x…

A: Recall: Integral of xndx = xn+1 / (n + 1)  + C

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

A: Consider the provided integral, ∫2-3x10dx Find the indefinite integral and check the result by…

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

A: ∫7x1-x23dxTake the constant out:  ∫a·fxdx=a·∫fxdx=7·∫x1-x23dxSubs u = 1-x2=7·∫ -12u3duTake the…

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

A: Given: I=∫sec2x2tanx2dx

Q: Evaluate the definite integral. dx 6x --

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Q: x4/3' dx -1 | --

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

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Q: Find the integral: x45-x5 dx

A: The objective is to find the integration.

Q: find integral  sqrt ( x2 - 9 )dx

A: Given: I=∫x2-9dx we know that ∫x2-a2dx=x2x2-a2-a22lnx+x2-a2+c                                ..1

Q: 6) S(x + 2)dx

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

A:

Q: Find the indefinite integral and check the results by differentiation? (4x^2 + 3)^2

A: I=∫(4x2+3)2dx =∫(16x4+24x2+9)dxintegrateI=165x5+8x3+9x+c    where c is any constant

Q: Find the indefinite integral and check the result by differentiation                     ∫7x / (1 −…

A: ∫xndx=xn+1n+1+C

Q: |(4x2 + 3)?dx

A:

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

A: Given, I=∫x2-932x dx

Q: Find the indefinite integral and check the result by differentiation                     ∫x3(x4 +…

A: ∫x3x4+32 dx Put, x4+3=t⇒4x3+0=dtdx⇒4x3 dx=dt⇒x3 dx=dt4 Therefore, ∫x3x4+32 dx=∫t2 dt4=14∫t2…

Q: Find the indefinite integral and check the result by differentiation                     ∫x2 / (1 +…

A: Find the indefinite integral and check the result by differentiation                     ∫x2 / (1 +…

Q: Find the indefinite integral and check the results by differentiation |(4x² + 3)*dx

A: Given integral is∫4x2+32dx. ∫4x2+32dx=∫16x4+24x2+9dx=16x55+24x33+9x+C=16x55+8x3+9x+C

Q: Find the indefinite integral and check the result by differentiation                 ∫5x 3√(1 − x2)…

A: Given integral is ∫5x31-x2dx.

Q: tan 0 . Find the indefinite integral by using the substitution x = xp: (1+ x2)?

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Q: Find the indefinite integral and check the result by differentiation.              ∫(13 − x) dx

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Q: Find the indefinite integral and check the result by differentiation                     ∫ x /√(1 −…

A: Given indefinite integral ∫x1-x2dx Substitute the value of 1-x2=t and differentiate it w.r.t "x"…