Mathematics

$$\int { \left( { x }^{ 2 }-5x+7 \right)  } dx$$


SOLUTION

We have,

$$\int{\left( {{x}^{2}}-5x+7 \right)dx}$$

We have,

$$ \int{\left( {{x}^{2}}-5x+7 \right)}dx $$

$$ \Rightarrow \int{{{x}^{2}}}dx-5\int{xdx}+7\int{1dx} $$

$$ \Rightarrow \dfrac{{{x}^{3}}}{3}-5\dfrac{{{x}^{2}}}{2}+7x+C $$

Hence, this is the answer.
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 86
Enroll Now For FREE

Realted Questions

Q1 Single Correct Medium
$$\int \sqrt {1+x^2}dx$$ is equal to
  • A. $$\dfrac {2}{3}(1+x^2)^{\frac {2}{3}}+C$$
  • B. $$\dfrac {2}{3}x(1+x^2)^{\frac {3}{2}}+C$$
  • C. $$\dfrac {x^2}{2}\sqrt {1+x^2}+\dfrac {1}{2}x^2log |x+\sqrt {1+x^2}|+C$$
  • D. $$\dfrac {x}{2}\sqrt {1+x^2}+\dfrac {1}{2}log|+\sqrt {1+x^2}|+C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Single Correct Hard
The anti-derivative of $$ f(x)=\log(\log x)+ (\log x)^{-2}$$ whose graph passes through $$(e,e)$$ is
  • A. $$x[\log(\log x)+ (\log x)^{-1}]$$
  • B. $$x[-\log(\log x) +(\log x)^{-1}]+e$$
  • C. $$x[\log(\log x)-(\log x)^{-1}]+3e$$
  • D. $$x[\log(\log x) -(\log x)^{-1}]+2e$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Single Correct Medium
Resolve $$\displaystyle \frac{x^4}{(x-1)^4(x+1)}$$ into partial fractions.
  • A. $$\displaystyle \frac{1}{2(x-1)^4}-\frac{7}{4(x-1)^3}+\frac{17}{8(x-1)^2}+\frac{15}{16(x-1)}+\frac{1}{16}\cdot\frac{1}{(x+1)}$$
  • B. $$\displaystyle \frac{1}{2(x-1)^4}+\frac{5}{4(x-1)^3}+\frac{17}{8(x-1)^2}+\frac{15}{16(x-1)}+\frac{1}{16}\cdot\frac{1}{(x+1)}$$
  • C. $$\displaystyle \frac{1}{2(x-1)^4}+\frac{7}{4(x-1)^3}+\frac{13}{8(x-1)^2}+\frac{15}{16(x-1)}+\frac{1}{16}\cdot\frac{1}{(x+1)}$$
  • D. $$\displaystyle \frac{1}{2(x-1)^4}+\frac{7}{4(x-1)^3}+\frac{17}{8(x-1)^2}+\frac{15}{16(x-1)}+\frac{1}{16}\cdot\frac{1}{(x+1)}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Subjective Medium
Evaluate $$\displaystyle \overset{2}{\underset {0}{\int}} e^x dx$$ as a limit of sum.

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