No written by hand solution Show that \[ \mathcal{L}\left\{\frac{f(t)}{t}\right\}(s)=\int_{s}^{\infty} F(\sigma) d \sigma \] where \[ F(\sigma)=\mathcal{L}\{f\}(\sigma)=\int_{0}^{\infty} e^{-\sigma t} f(t) d t \]

Q: Evaluate definite integral. \int_{0}^{\pi / 4} \sec ^{2} x d x\end{array

A: Given: ∫0π4sec2xdx

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A:

Q: integral of (e^tan(sqrt of x))/(sqrt of x)(cos^2)(sqrt of x)dx with an upper limit of pi^2 and a…

A:

Q: show that the antiderivatives are equivalent. \int \frac{6}{4+9 x^{2}} d x=\arctan \frac{3 x}{2}+C…

A: To show: Antiderivatives are equivalent. Given: Antiderivative of ∫64+9x2dx=tan-13x2+C or…

Q: Suppose f(0.25)=f(0.75)=b. If the Composite Trapezoidal rule with n=2 gives the value 4 for \int_0^1…

A: Introduction: The trapezoidal rule is a method to approximate a definite integral numerically. In…

Q: Sketch an approximate graph of g onthe interval0<=x<=4 g(x)=\int_{0 }^{x}( f(t)) d t Identify…

A: Let F be the anti-derivative of the function f. Calculate the indefinite integral of ft with respect…

Q: Evaluate the integral. So (sint)i + + jdt © 2(x + 1)] - 2ª − ln (x + 1)] -21--- +1 21+ln(x+1) j

A: The given integral is [(sint) i + 1 /(t+ 1 )j], limit from 0 to pi.

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

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Q: It is true that int -1 ^ 1 int 0 ^ sqrt 1-x^ 2 dydx= int 0 ^ pi int 0 ^ 1 r drd theta=2 int 0 ^ pi/2…

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Q: f*g = \int _0^1 f(x)g(x)dx By computing the above dot product for each of the six possible pairs^1,…

A: Here, the given definition of the dot product is: f·g=∫01f(x) g(x) dx

Q: Use trapezoidal with 3 level romberg (k=3) to evaluate the integral from lower limit 0 to upper…

A:

Q: what the limt \lim_(n->\infty )\sum_(i=1)^n ((2)/(x_(i)^(2))) as a definite integral over the…

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Q: Suppose that \int_(-1)^3 f(x)dx=-4=\int_(-1)^3 2g(x)dx. If k is a constant and \int_(-1)^3…

A: We need some basic properties of Integration. Let us discuss them.

Q: (a) \int (8x^(2)+3x\sqrt(x)+(6x+6)/(\sqrt(x)))dx=,+C.

A: since you have posted multiple questions in this question which are not interlinked so i have solved…

Q: Evaluate the following integral:  \int _1^7\left(t^2+3\right)cos\left(5t\right)dt

A:

Q: Find the first order moment of pdf f(x) = (X^2)(x)[e^(-^x)], x 2 O, and O elsewhere. O /2 2/A O…

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Q: Mrs. Wigen conducted a survey in her math class. She asked each of her students to tell her how many…

A: The data plotting helps to visualize the relationship between variables. A dot plot consists data,…