Can you find the area of the region?

Question

y = 81 - x^4

Answer 1

Area = ∫_{(from -3 to 3)} [81 - x⁴]dx

= 2∫_{(from 0 to 3)}[81 - x⁴]dx = 2(81x - (1/5)x⁵)_{(from 0 to 3)}

= 2(243 - 243/5) = 388.8

Answer 2

The integral is 81x - (1/5)x^5

x-->3 : 81*3 - (1/5)(3^5) = 243 - 243/5 = 162

x-->-3: 81*-3 - (1/5)(-3)^5 = -243 - (-243/5) = 243/5 - 243 = -162

The area is 162- -162 = 324

Again, as a sanity check, there are TWO right triangles with height 80 and base 3.

That is 2 * (1/2) * 80 * 3 = 240