Consider ∫ 0 x ( t 2 − 8 t + 13 ) d t = x sin ( x a ) and ( a , x ∈ R − { 0 }) x takes the values for which the equation has a solution, then the number of values of a ∈ [ 0 , 100 ] is ____

Question

Consider ∫ 0 x ​ ( t 2 − 8 t + 13 ) d t = x sin ( x a ​ ) and ( a , x ∈ R − { 0 }) x takes the values for which the equation has a solution, then the number of values of a ∈ [ 0 , 100 ] is ____

TestHub · Accepted Answer

( 3 t 3 ​ − 2 8 t 2 ​ + 13 t ) 0 x ​ = x sin ( x a ​ ) x { 3 x 2 ​ − 4 x + 13 − sin ( x a ​ ) } = 0 Here x  = 0 ⇒ 3 1 ​ ( x 2 − 12 x + 39 ) = sin ( x a ​ ) ​ ⇒ 3 1 ​ ( x − 6 ) 2 + 1 = sin ( x a ​ ) ​ ⇒ 6 a ​ = 2 π ​ or 2 5 π ​ or 2 9 π ​ ​ ∴ a = 3 π , 15 π , 27 π ( 3 values ) ​

Mathematics - Functions Question with Solution | TestHub

Options:

Doubts & Discussion