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GATE Mathematics 2020Q. 12 · 2 marks
Let f(x) = x² on [0, 1]. Then the value of ∫₀¹ f(x) dx is
AB ✓CD
Solution
1Write the integral and apply the power rule
∫₀¹ x² dx = [ x³ / 3 ]₀¹
2Evaluate at the limits, subtract
= 1/3 − 0 = 1/3
Concept · the power rule for definite integrals.
Shorter method · for ∫₀¹ xⁿ dx the answer is always 1/(n+1).
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General Aptitude
Q. 1 – 10
Mathematics
Q. 11 – 25
Q. 26 – 55
Q. 12 Let f(x) = x² on [0, 1]. Then ∫₀¹ f(x) dx is
Solution
1Apply the power rule
∫₀¹ x² dx = [ x³ / 3 ]₀¹
2Evaluate at the limits
NotePower rule: raise the power by one, then divide by it.