Find the integral of \(8x^3+1\).

Category: QuestionsFind the integral of \(8x^3+1\).
Editor">Editor Staff asked 11 months ago

Find the integral of \(8x^3+1\).
 
(a) 2x^4+x+C
 
(b) 2x^6-5x+C
 
(c) 2x^4-x+C
 
(d) 2x^4+x^2 C
 
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This interesting question is from Integration as an Inverse Process of Differentiation topic in chapter Integrals of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 11 months ago

Right option is (a) 2x^4+x+C
 
Explanation: \(\int \,8x^{3+1} \,dx\)
 
Using \(\int \,x^n \,dx=\frac{x^{n+1}}{n+1}\), we get
 
\(\int \,8x^{3+1} \,dx=\int 8x^3 \,dx+\int \,1 \,dx\)
 
=\(\frac{8x^{3+1}}{3+1}+x\)
 
=\(\frac{8x^4}{4}+x\)
 
=2x^4+x+C.