Home › UP Board Class 12 › mathematics › Integrals › The definite integral $\int_0^1 x\, dx$ equals:
The definite integral $\int_0^1 x\, dx$ equals:
A$1$, the integral of the constant function over $[0, 1]$
B$1/2$, since $F(x) = x^2/2$ gives $F(1) - F(0) = 1/2$
C$0$, since the antiderivative vanishes at the endpoints here
D$2$, mistakenly doubling the answer on the school chart
Answer & Solution
Correct answer: B. $1/2$, since $F(x) = x^2/2$ gives $F(1) - F(0) = 1/2$
$F(x) = x^2/2$; $F(1) - F(0) = 1/2 - 0 = 1/2$.
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