First slide

Introduction to integration

Question

If $f (x) = 1 + 3^{x} \log 3$ and $F (x)$ be its antiderivative which assume the value $7$ for $x = 2 .$ The value of $x$ for which the curve $F (x)$ cuts the abscissa axis is

Easy

A

0
B

1
C

2
D

3

Solution

$F (x) = \int f (x) d x + C = x + 3^{x} + C but F (2) =$ $7 so 7 = 2 + 9 + C$
$\Rightarrow C = - 4 .$ Hence $F (x) = x + 3^{x} - 4$ Now $F (x) = 0$
$\Rightarrow x = 1$

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