What-is-1-3-1-x-4-dx-equal-to-a-232-5-b-116-5-c-116-5-d-232-5-

Question Number 12303 by Gaurav3651 last updated on 18/Apr/17

W h a t i s \underset{1}{\int^{3}} ∣ 1 - x^{4} ∣ d x e q u a l t o ?

(a) - 232 / 5

(b) - 116 / 5

(c) 116 / 5

(d) 232 / 5

Answered by ajfour last updated on 18/Apr/17

Missing \left or extra \right

= (\frac{3^{5}}{5} - 3) - (\frac{1}{5} - 1)

= \frac{243}{5} - \frac{1}{5} - 3 + 1

= \frac{242}{5} - 2 = \frac{232}{5} . (d) .

Commented by prakash jain last updated on 22/Apr/17

For module problem you need

to approach in the following way

∣ f (x) ∣ find range of x for which f (x) ⩾ 0

∣ f (x) ∣ find range of x for which f (x) < 0

Split the definite integral in parts

where f (x) ⩾ 0 and where f (x) < 0

replace ∣ f (x) ∣ by f (x) or - f (x)

For example

\int_{0}^{3} ∣ 1 - x^{2} ∣ d x

∣ 1 - x^{2} ∣⩾ 0 for x \in [0, 1]

∣ 1 - x^{2} ∣< 0 for x \in (1, 3]

\int_{0}^{3} ∣ 1 - x^{2} ∣ d x = \int_{0}^{1} (1 - x^{2}) d x + \int_{1}^{2} - (1 - x^{2}) d x

Commented by Gaurav3651 last updated on 19/Apr/17

{s h o u l d n}^{'} t w e p r o c e e d i n d i f f e r e n t

w a y t o s o l v e m o d u l u s p r o b l e m s

o t h e r w i s e i t i s s i m i l a r t o

\underset{1}{\int^{3}} (x^{4} - 1) d x