Mathematics

If $$\int^{a}_{1} (3x^2+2x+1)dx=11$$, find real values of a.


SOLUTION
We know,

$$\displaystyle \int^{a}_{1}(3x^2+2x+1)dx$$

we know that $$\displaystyle\int{{x}^{n}dx}=\dfrac{{x}^{n+1}}{n+1}+c$$

$$\Rightarrow [x^3+x^2+x]^{a}_{1}=11$$

$$\Rightarrow (a^3+a^2+a)-(1+1+1)=11$$

$$\Rightarrow a^3+a^2+a-3=11$$

$$\Rightarrow a^3+a^2+a-14=0$$

$$\Rightarrow (a-2)(a^2+3a+7)=0$$

since $$a^2+3a+7$$ does not have real values as its $$D=3^2-4(2)(7)=-47<0$$

$$\therefore a=2$$
View Full Answer

Its FREE, you're just one step away


Subjective Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84
Enroll Now For FREE

Realted Questions

Q1 One Word Medium
$$\displaystyle I= \int_{0}^{\pi /2}\frac{x\sin x\cos x}{\cos ^{4}x+\sin ^{4}x}dx$$
$$\displaystyle \therefore I= \pi ^{2}/k.$$
what is k?

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Single Correct Medium
If $$I= \displaystyle \int_{-2}^{2}\displaystyle \frac{e^{x}}{e^{x}+e^{-x}}\: dx$$ then $$I$$ is equal to?
  • A. $$4$$
  • B. $$3$$
  • C. $$0$$
  • D. $$2$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Single Correct Hard
The value of $$\int \dfrac {10^{x/2}}{\sqrt {10^{-x} - 10^{x}}}\, dx$$ is
  • A. $$2\sqrt {10^{-x} + 10^{x}} + c$$
  • B. $$\dfrac {1}{\log_{e}10}\sin h^{-1} (10^{x}) + c$$
  • C. $$\dfrac {-1}{\log_{e}10}\sin h^{-1}(10^{x}) + c$$
  • D. $$\dfrac {1}{\log_{2}10}\sin^{-1}(10^{x}) + c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Medium
$$\displaystyle \int\frac{dx}{x\sqrt{1-x^{3}}}=$$
  • A. $$\dfrac{1}{3}\log|\displaystyle \frac{\sqrt{1-x^{2}}+1}{\sqrt{1-x^{2}}-1}|+c$$
  • B. $$\dfrac{1}{3}\log|\displaystyle \frac{1}{\sqrt{1-x^{3}}}|+c$$
  • C. $$\displaystyle \frac{1}{3}\log|1-x^{3}|+c$$
  • D. $$\dfrac{1}{3}\log|\displaystyle \frac{\sqrt{1-x^{3}}-1}{\sqrt{1-x^{3}}+1}|+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Passage Medium
Consider two differentiable functions $$f(x), g(x)$$ satisfying $$\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$$ & $$\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$$. where $$\displaystyle f(x)>0    \forall  x \in  R$$

On the basis of above information, answer the following questions :

Asked in: Mathematics - Limits and Derivatives


1 Verified Answer | Published on 17th 08, 2020

View Answer