Use (a) the Trapezoidal Rule integral 1to 4    sqrt x cos x dx                 with n= 8

Q: J X √9 - x² dx

A:

Q: Find the value of the integral x²dx (x² + 9)(x² + 4)² 0-

A: The integral can be solved by first simplifying the integrand by partial fraction decomposition.…

Q: Use contour integration to evaluate 6.00 sin x x(x² + 1)² -dx.

A:

Q: Express in exact form: In(x² + 1)dx

A: The definite integral is given as .The aim is to express this form in exact form.Concept used :Apply…

Q: Use (a) the Trapezoidal Rule integral 1to 4    cos  2  x dx                 with n= 8

A: Given Data The integral is . The number of intervals is n=8.   The function of the given integral…

Q: 1 Evaluate the integral S√I+2x f dx

A: We have definite integral  Substitute 1+2x=z2  to make integration radical free as I have done…

Q: Integral: Evaluate -2 sin 2x xp= V9+ cos² 2x

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Q: i) S, (x Inx)³ dx. ii) S •1 3 In) dx.

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Q: (e) S, In|x| dx.

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Q: 1=[", 64 cos(nx) dx x* -16 -08-

A: We have given integral, I=∫-∞∞64cos(πx)dxx4-16 We need to solve that integral.

Q: EX: using the relation I= Vn show that J1(x) = 2 sin x

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Q: S 1 dx (2x - 3)²

A:

Q: 4 (2x + 6)*dx -3

A:

Q: V22 + 10x + x² dx

A:

Q: Evaluate f(x) = 7sin r 1 COS -X %3D at a /3. x =

A: Given fx=7sinx-cos12x To evaluate the value of function at x=π3 put this value in fx fx=7sinx-cos12x

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.