Approximate the integrals (1₁ cos xdx using Gauss-Legendre quadrature with n=3

Q: Find the indefinite integral J J9+x? dx using an appropriate trigonometric substitution.

A: Given :               I = x29-x2 dx         Substituting x = 3 sin u and dx = 3 cos u du

Q: Evaluate the integral I 3 cos (√t) √t dt

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Q: Evaluate the integrals

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Q: f(2 + Cos[2 vx ])dx V хр

A: Given the integral ∫022+Cos2xdx

Q: . +2 sec? (20 - ㅠ)) dθ 20- ㅠ

A:

Q: Consider the integral I=ſ¹₁(lnx) (arccosx)dx Let the primary branch of I be expressed as a+bi.…

A: The given integral is:The primary branch of I be expressed as a+bi.To find: b-a.Formula used:

Q: What is the integral of 10pi(4-y)(sqrt(siny))dy from 0 to pi?

A: Let I=∫0π10π4-ysinydy Then, ∫0π10π4-ysiny…

Q: Evaluate the integrals

A: 71). To evaluate the integral: ∫tan2x+sec2xdx Solution: We know that, sec2θ-tan2θ=1⇒tan2θ=sec2θ-1…

Q: Solve: The integrand (1-cos2 4t) cos4t dt on the integral 0 to pi/12

A: Use Pythagorean identity. 1-cos^2 theta = sin^2 thetahere theta= 4t

Q: arcsin 4y dy 1 – 16y2

A: Given: ∫arcsin4y1-16y2dy

Q: 2, (6 + 3 cos x) dx Evaluate the following integral: a) Single application of the trapezoidal rule…

A: The given integral is ∫0π26+3cos xdx The trapezoidal formula  is ∫abf(x)dx=b-a2f(a)+f(b) The…

Q: 12 cos6x. sin³ xdxCalculate "/2 3 the integral

A: It is integral problem.

Q: Use integration by parts to find, x cos2x dx

A: Answer :

Q: Consider the function f (x) = cos (2x) a) Find the polynomial of degree 4 centered at X = 1.…

A: The given function is fx=cos2x

Q: Evaluate the given integral using Trigonometric Substitution 27e#dæ (6e# –9e2z +10)

A: Given integration is                                     ∫27 e4xdx6ex-9e2x+10 The formula for…

Q: Use Wallis’s Formulas to evaluate the integral.

A: Wallis's formula for integration for even n: ∫0π/2cosnx dx=12·34… n-1nπ2

Q: sin° (2æ) cos(2æ)dæ

A: