Mathematics

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

##### SOLUTION

We have,

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

We have,

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

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

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

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### 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. $\dfrac {x}{2}\sqrt {1+x^2}+\dfrac {1}{2}log|+\sqrt {1+x^2}|+C$

1 Verified Answer | Published on 17th 09, 2020

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. $x[\log(\log x) -(\log x)^{-1}]+2e$

1 Verified Answer | Published on 17th 09, 2020

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. $\displaystyle \frac{1}{2(x-1)^4}+\frac{7}{4(x-1)^3}+\frac{17}{8(x-1)^2}+\frac{15}{16(x-1)}+\frac{1}{16}\cdot\frac{1}{(x+1)}$

1 Verified Answer | Published on 17th 09, 2020

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

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 $\displaystyle f(x)>0 \forall x \in R$