Question

The value of the integral ${\int }_0^1\left\{4t^3{\left(1+t\right)}^8+8t^4{\left(1+t\right)}^7\right\}dt$ is

• A. $128$
• B. $512$
• C. $256$
• D. $1024$

Answer 1

Answer: (C)

Note that $\frac{d}{dt}\left\{t^4{\left(1+t\right)}^8\right\}=4t^3{\left(1+t\right)}^8+8t^4{\left(1+t\right)}^7$
Hence, the required integral is
${t^4(1+t{)}^8|}_0^1=2^8$