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Black Advanced Problems in Mathematics

Exam: Black Advanced Problems in Mathematics
Subject: Mathematics
Chapter: Indefinite and Definite Integration

Black Advanced Problems in Mathematics · Mathematics · Indefinite and Definite Integration

Paragraph for Question Nos. 12 to 13 Let f_0(x) = x and for n ≥...

**Paragraph for Question Nos. 12 to 13** Let

f_0(x) = \ln x

and for

n \ge 0

and

x > 0

Let

f_{n+1}(x) = \int_0^x f_n(t) dt

then :

f_3(x)

equals :

Options

A $\frac{x^3}{3} \left( \lnx - \frac{5}{6} \right)$
B $\frac{x^3}{3} \left( \lnx - \frac{11}{6} \right)$
C $\frac{x^3}{6} \left( \lnx - \frac{11}{6} \right)$
D $\frac{x^3}{6} \left( \lnx - \frac{5}{6} \right)$

Correct answer

C. $\frac{x^3}{6} \left( \lnx - \frac{11}{6} \right)$

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