Solveeit Logo
Login

Question

Question: If g(x) = \(\int_{0}^{x}{\cos^{4}tdt}\), then g(x + p) equals-...

If g(x) = ∫0xcos⁡4tdt\int_{0}^{x}{\cos^{4}tdt}, then g(x + p) equals-

A

g(x) + g(p)

B

g(x) – g(p)

C

g(x) . g(p)

D

0

Answer

g(x) + g(p)

Explanation

Solution

g(x + p) = ∫0x+πcos⁡4(t)dt\int_{0}^{x + \pi}{\cos^{4}(t)dt}

= ∫0xcos⁡4(t)dt\int_{0}^{x}{\cos^{4}(t)dt}+ ∫xx+πcos⁡4tdt\int_{x}^{x + \pi}{\cos^{4}tdt} ... (3)

= ∫0xcos⁡4tdt\int_{0}^{x}{\cos^{4}tdt}+ ∫0πcos⁡4tdt\int_{0}^{\pi}{\cos^{4}tdt} (Q cos4 t is periodic function)

= g(x) + g(p)