Q. 154.8( 5 Votes )

Evaluate: <

Answer :


Using



sin(π – x) = sinx and cos(π – x) = -cosx



Add (i) and (ii)





Substitute cosx = t


When x = 0 t = 1 and when x = π t = -1


Differentiate t = cosx with respect to x



-dt = sinxdx


Put in (a)



Using




I = 2π[tan-1(1) – tan-1(-1)]





I = π2


Hence


OR



Multiply and divide by 2,







I = 1/2(I1 – I2) …(i)


Let us first solve I1



Substitute x2 + 5x + 6 = t


Differentiate with respect to x



dt = (2x + 5)dx






I1 = 2√t


Resubstitute t



Now let us find I2





Using the result




Put I1 and I2 value in (i)


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