Home › UP Board Class 12 › mathematics › Integrals › The AREA bounded by y = x² and the x-axis from x…
The AREA bounded by y = x² and the x-axis from x = 0 to x = 3 is:
A$3$ (using only the upper limit)
B$6$ (twice the upper limit value)
C$9$ (using anti-derivative properly)
D$27$ (cubing the upper limit)
Answer & Solution
Correct answer: C. $9$ (using anti-derivative properly)
Area = ∫_0^3 x² dx = [x³/3] from 0 to 3 = 27/3 − 0 = 9.
Related questions
$\displaystyle\int_2^3 \dfrac{x\,dx}{x^2+1}$ equals$\displaystyle\int_0^{2a} f(x)\,dx$ equals $2\displaystyle\int_0^{a} f(x)\,dx$ precisely wIf $f(a+b-x)=f(x)$, then $\displaystyle\int_a^b x\,f(x)\,dx$ is equal to$\displaystyle\int \frac{dx}{e^{x}+e^{-x}}$ is equal toA rational function $\dfrac{P(x)}{Q(x)}$ is called proper when$\displaystyle\int_0^{\pi/4} \tan x\,dx$ equals$\displaystyle\int_0^{1} x e^{x^2}\,dx$ equalsThe value of $\displaystyle\int_0^{\pi/2} \log\!\left(\dfrac{4+3 in x}{4+3\cos x}\right)dx