integral[7 sqrt 2/2,0]sqrt(49+x^2) dx
x = 7 sinh(t)
sqrt(49 + x^2) = 7 sqrt[1 + sinh^2(t)] = 7 cosh(t)
dx = 7 cosh(t) dt
The integral is thus:
49 Integral of cosh^2(t) dt =
49 Integral of [cosh(2t) + 1]/2 dt =
49 [t/2 + 1/4 sinh(2t)]
sqrt(49 + x^2) = 7 sqrt[1 + sinh^2(t)] = 7 cosh(t)
dx = 7 cosh(t) dt
The integral is thus:
49 Integral of cosh^2(t) dt =
49 Integral of [cosh(2t) + 1]/2 dt =
49 [t/2 + 1/4 sinh(2t)]