Download App

Definite Integrals — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integrals2 Marks
Question
Write the coefficient a, b, c of which the value of the integral $\int\limits^3_{-3}(\text{ax}^2+\text{bx}+\text{c})\text{dx}$ is independent.
✓

Answer

$\int\limits^3_{-3}(\text{ax}^2+\text{bx}+\text{c})\text{dx}$$=\Big[\text{a}\frac{\text{x}^3}{3}+\text{b}\frac{\text{x}^2}{2}+\text{cx}\Big]^3_{-3}$
$=9\text{a}+\frac{9}{2}\text{b}+3\text{c}+9\text{a}-\frac{9}{2}\text{b}+3\text{c}$
$=18\text{a}+6\text{c}$
Hence, the given integral is independent of b.

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 "Solve the Following Question.(2 Marks)" from Definite Integrals→Definite Integrals — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Integrate the following functions w. r. t. x

$\int \frac{1}{3-2 \cos 2 x} \cdot d x$

→
Write the converse and contrapositive of the following statements.

“If a function is differentiable then it is continuous”

→
If $F(x)=G\{3 G[5 G(x)]\}, G(0)=0$ and $G^{\prime}(0)=3$, find $F^{\prime}(0)$.
→
If $\vec{\text{a}}=\hat{\text{i}}-\hat{\text{j}}$ and $\vec{\text{b}}=-\hat{\text{j}}+2\hat{\text{k}},$ find $\big(\vec{\text{a}}-2\vec{\text{b}}\big).\big(\vec{\text{a}}+\vec{\text{b}}\big).$
→
A factory produces bulbs. The probability that one bulb is defective is $\frac{1}{50}$ and they are packed in boxes of 10. From a single box, find the probability that.
exactly two bulbs are defective.
→
Find the angle between the line $\bar{r}=(\hat{i}+2 \hat{j}+\hat{k})+\lambda(\hat{i}+\hat{j}+\hat{k})$ and the plane $\bar{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=8$
→
Find the area of parallelogram whose diagonals are determined by the vectors $\bar{a}=$$3 i-\hat{j}-2 \hat{k}_{\text {t }}$ and $\bar{b}=-\hat{i}+3 \hat{j}-3 \hat{k}$
→
Using determinants prove that the points $(a, b), (a', b)$ and $(a - a', b - b')$ are collinear if $ab' = a'b$.
→
Show that the points $(1,1,1)$ and $(-3,0,1)$ are equidistant from the plane $\bar{L}(3 \bar{i}+4 \bar{\jmath}-12 \bar{k})+13=0$
→
Find the cosine of the angle between the vectors $4\hat{\text{i}}-3\hat{\text{j}}+3\hat{\text{k}}$ and $2\hat{\text{i}}-\hat{\text{j}}-\hat{\text{k}}.$
→