Question

4. (10 pts.) Approximate the following integrals using 2-point Gauss quadrature, and compare to the exact value (hint: You need to perform a change of variables. In my solution I will do a general change of variables and then write a MATLAB code to implement it.) (a) ??¹ x³ + 2x dx (b) ??? x / ?(x² + 9) dx (c) ??? ln(x) dx (d) ???² x? dx (e) ???³ e^(-x² / 2) dx.

          4. (10 pts.) Approximate the following integrals using 2-point Gauss quadrature, and compare to the exact value (hint: You need to perform a change of variables. In my solution I will do a general change of variables and then write a MATLAB code to implement it.)

(a) ??¹ x³ + 2x dx
(b) ??? x / ?(x² + 9) dx
(c) ??? ln(x) dx
(d) ???² x? dx
(e) ???³ e^(-x² / 2) dx.

4. (10 pts.) Approximate the following integrals using 2-point Gauss quadrature, and compare to the exact value (hint: You need to perform a change of variables. In my solution I will do a general change of variables and then write a MATLAB code to implement it.)

(a) ??¹ x³ + 2x dx
(b) ??? x / ?(x² + 9) dx
(c) ??? ln(x) dx
(d) ???² x? dx
(e) ???³ e^(-x² / 2) dx.

Added by Matthew R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

06/06/2023

Step 1

We can do this by using the following change of variables: $$x = \frac{b-a}{2}t + \frac{a+b}{2}$$ $$dx = \frac{b-a}{2}dt$$ Show more…

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Approximate the following integrals using 2-point Gauss quadrature, and compare to the exact value (hint: You need to perform a change of variables. In my solution I will do a general change of variables and then write a MATLAB code to implement it.) (a) ∫0^1 x^3 + 2x dx (b) ∫0^4 x / √(x^2+9) dx (c) ∫1^4 ln(x) dx (d) ∫-1^2 x^5 dx (e) ∫-3^3 e^(-x^2/2) dx.