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A curve y = f(x) passes through (1, 2) and satisfies x*dy/dx + y = b*x⁴. For what value of b is the integral of f(x) from x = 1 to x = 2 equal to 62/5?
- 5
- 10
- 62/5
- 31/5
Correct answer: 10
Solution
Recognising the left side as d(xy)/dx gives y = b x⁴/5 + C/x; using (1,2) fixes C, and the definite-integral condition forces b = 10.
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