Theory question 111
Integration(a) Evaluate ∫12 x/√(5 − x2) dx
(b) (i) Evaluate |2 −3 1|
|0 1 −2|
|1 2 −3|
(ii) Using your answer in (b)(i), solve the simultaneous equations
2x − 3y + z = 10
y − 2z = −7
x + 2y − 3z = −9
Show the model answer
Model answer
(a) Let u = 5 − x2: integral = [−√(5 − x2)] from 1 to 2 = −1 + 2 = 1
(b)(i) 2(−3 + 4) + 3(0 + 2) + 1(0 − 1) = 7
(ii) Cramer's rule: Δx = 14, Δy = −7, Δz = 21
x = 2, y = −1, z = 3
Explanation
Use the substitution u = 5 − x²; for the equations use Cramer's rule with the determinant from (b)(i).