The correct option is A 3x^22 5x+C We know that, ∫( P+Q ) dx =∫ Pdx +∫ Qdx ∫ kPdx =k∫ Pdx #160; #160; #160; where k is a constan ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Implicit Differentiation

Evaluate: ∫...

Question

Evaluate: $\int 3 x - 5 d x$

\frac{3 x^{2}}{2} - 5 x + C

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{3 x^{2}}{2} - 7 x + C

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{3 x^{2}}{2} - 4 x + C

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{3 x^{2}}{2} - 6 x + C

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{3 x^{2}}{2} - 5 x + C$
We know that,
$\int (P + Q) d x = \int P d x + \int Q d x$
$\int k P d x = k \int P d x$ {where $k$ is a constant}
Hence ,
$\int (3 x - 5) d x = 3 \int x d x - 5 \int d x$
$\Rightarrow \int x d x = \frac{x^{2}}{2} + C_{1} & \int d x = x + C_{2} ∵ \int x^{n} d x = \frac{x^{n + 1}}{n + 1} + C ∴ \int (3 x - 5) d x = 3 \frac{x^{2}}{2} - 5 x + C$
{ $C$ is equal to $C_{1} + C_{2}$ }

Suggest Corrections

Similar questions

\frac{2 x}{{3 x}^{2} - x + 2} - \frac{7 x}{{3 x}^{2} + 5 x + 2} = 1

\frac{- a - \sqrt{b}}{c}

\frac{- a - \sqrt{b}}{c}

b - a - c

\int \frac{3 x + 7}{3 x^{2} + 14 x - 5} d x = \frac{1}{2} log | 3 x^{2} + 14 x - 5 | + c

\int \frac{f^{'} (x)}{f (x)} d x = log | f (x) | + c

\int \sqrt{3 x^{2} - 4 x + 5} d x

\int \frac{2 x + 3}{\sqrt{x^{2} + 4 x + 5}} d x

lim x \to - 2 \frac{x^{4} + 2 x^{3} + 3 x^{2} + 5 x - 2}{x^{5} + 3 x^{4} + 2 x^{3} + 3 x^{2} + 7 x + 2}

Join BYJU'S Learning Program