Evaluate f(x)dx where f(x) is defined by f(x) = {* 2x ifx<2 if x > 2 Verify this definite integral by using the graph of f(x) and properties of geometry.

Q: Find the indefinite integral.

A: We find this indefinite integral by the method of substitution. We re-write the integral in a…

Q: Find the indefinite integral by using the substitution x = tan 0 (1+ x2)2dx

A:

Q: x° ln x dx

A: Let us find the value of ∫x3lnx dx. To integrate the given function we have to use the integration…

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: Evaluate the definite integral by the limit definition

A: Here,

Q: -0.5 3. f5 x(1-x)³ dx 0

A: To evaluate the given definite integral by using substitution rule.∫00.5x1-x3 dx

Q: Find the indefinite integral using the substitution x = 2 tan θ.

A: The given integral is

Q: Find the indefinite integral and check the result by differentiation. S f (x) dx, where f (x) =(/¤-…

A:

Q: Find the indefinite integral ∫ x/√(1 − x4)   dx

A:

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

A: Given:

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

A:

Q: Use an indefinite integral to define a function F(x) having derivative e^cosx for all x and…

A:

Q: Let [ ·] represent the greatest integral function less than or equal to n tan x n sin x x. Then,…

A:

Q: 23. (x + 1)(3x – 2) dx

A:

Q: 17. x dx

A:

Q: Find the indefinite integral ∫ (x2 − 2x) / (x3 − 3x2) dx

A: Given: ∫x2-2xx3-3x2dx for solving this integral we substitute  x3-3x2=t now differentiate both side…

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 the result by differentiation

A: Given: ∫x5x23dx for finding given integral, we substitute  x2=t…

Q: Evaluate the definite integral by the limit definition

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Evaluate the definite integral 2 x* +3x' -dx 1

A:

Q: Evaluate the indefinite integral: ∫x(x2 − 4) dx

A: We know that, ∫af(x)+bg(x) dx=a∫f(x) dx+b∫g(x) dx where a, bare constants , f, gare functions.…

Q: Find the indefinite integral and check the result by differentiation. (Use C for the constant of…

A:

Q: Find the indefinite integral.

A: Given integral: ∫x2-2xx3-3x2dx

Q: Find the indefinite integral and check the result by differentiation. ∫ 1/x5 dx

A:

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

A: Explanation: Given that, ∫x2(6-x3)5dx   Substitute the  u=6-x3du=-3x2dxdx=du-3x2   Now put this…

Q: Evaluate the indefinite integral. -dx 1 – x8

A: We use the standard integration result ∫11-x2dx=sin-1x+C

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

A:

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 and check the result by differentiation. (Use C for the constant of…

A:

Q: Evaluate the definite integral. Use a graphing utility to verify your result

A: Given integral ∫45x2x-6dx Substitute  u=2x-6 Upper limit at x=5 is 2. Lower limit at x= is 2…

Q: Evaluate the indefinite integral.

A:

Q: Find the indefinite integral and check the result by differentiation. ∫(x + 7) dx

A:

Q: Evaluate integral 0 to 3 (x 3 -6x) dx

A:

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

A: ∫xndx=xn+1n+1+C

Q: Find the general indefinite integral. x* + 4x +1

A:

Q: Evaluate the definite integral by the limit definition.

A: Given: ∫031-2x2dx

Q: Evaluate the indefinite integral x5 - 5x dx x3

A: This is a simple question related to integration  Solution is given below

Q: Evaluate the definite integral. 2x+ dx x² +x* +1

A: The given integral is ∫012x3+xx2+x4+1dx. Solve the given integration by integration by substitution…

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: Show, using the formula for the derivative of the inverse of a function,that the derivative of…

A: The solution of above question is written below.

Q: Find the indefinite integral ∫x+1√xdx.

A:

Q: Find the indefinite integral using any method ∫√(1 + √x) dx

A: Given: ∫ 1+x dxBy using the Substitution methods:Put   1+x =t…

Q: Find the indefinite integral. ∫(ln x)2/xdx

A: Given integral: ∫lnx2xdx Substitute t=ln(x) and differentiate it w.r.t 'x'…

Q: Find the indefinite integral using the formulas from Theorem "Differentiation and Integration…

A:

Q: Evaluate the indefinite integral x5 – 5x dx x3

A:

Q: Find the indefinite integral of (x2-cos x) dx

A:

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

A:

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"…

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.