If ^ a _03x^2 dx=8, Write the value of a. - Vidyadip

Question

If $\int\limits^{\text{a}}_03\text{x}^2\text{ dx}=8,$ Write the value of a.

✓

Answer

We have,
$\int\limits^{\text{a}}_03\text{x}^2\text{ dx}=8$
$\Rightarrow\Big[3\frac{\text{x}^3}{3}\Big]^{\text{a}}_0=8$
$\Rightarrow\big[\text{x}^3\big]^{\text{a}}_0=8$
$\Rightarrow\text{a}^3-0=8$
$\Rightarrow\text{a}=\sqrt[3]{8}$
$\Rightarrow\text{a}=2$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from INTEGRALS→INTEGRALS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\hat{\text{a}},\hat{\text{b}}$ are unit vectors such that $\hat{\text{a}}+\hat{\text{b}}$ is a unit vector, write the value of $\big|\hat{\text{a}}-\hat{\text{b}}\big|.$

Construct a $3 \times 4$ matrix $A = [a_{ij}]$ whose element $a_{ij}$ are given by:
$\text{a}_\text{ij}=\frac{1}{2}|-3\text{i}+\text{j}|$

If $|\vec{\text{a}}|=2,\big|\vec{\text{b}}\big|=5$ and $\vec{\text{a}}.\vec{\text{b}}=2,$ find $\big|\hat{\text{a}}-\hat{\text{b}}\big|.$

Evaluate the integral $\int_{-1}^{1} \frac{d x}{x^{2}+2 x+5}$ using substitution.

A bag contains 6 black and 3 white balls. Another bag contains 5 black and 4 white balls. If one ball is drawn from each bag, find the probability that these two balls are of the same colour.

Find area of the triangle with vertices at the point given (1, 0), (6, 0), (4, 3).

In the following matrix equation use elementary operation $R_2 → R_2 + R_1$ and the equation thus obtained:$\begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix}=\begin{bmatrix} 1 & 0 \\ 2 & -1 \end{bmatrix}\begin{bmatrix} 8 & -3 \\ 9 & -4 \end{bmatrix}$

If $\text{A}=\begin{bmatrix}1\\2\\3\end{bmatrix},$ write $AA^T$.

Show the feasible region under the constraints :
$
\begin{aligned}
2 x+y & \leq 6 \\
x & \geq 0 \\
y & \geq 0
\end{aligned}
$

Find a vector $\vec{\text{a}}$ of magnitude $5\sqrt2$, making an angle of $\frac{\pi}4$ with x-axis, $\frac{\pi}2$ with y-axis and an acute angle $\theta$ with z-axis.