Title Integration-2 & Animal diversity- Daily-16 MCQ (Home Practice)-With Solve.pdf ✅

3 15. y = 1 (4x + 1) 2 eμ‡iLv, y = 0, x = 0 Ges x = 2 †iLvÎq Øviv mxgve× †ÿ‡Îi †ÿÎdj KZ eM© GKK? 1 8 1 9 2 9 3 8 DËi: 2 9 e ̈vL ̈v:  2 0 1 (4x + 1) 2 dx =     (4x + 1)  2 + 1 ( 2 + 1)  4 2 0 =  1 4     1 4x + 1 2 0 =  1 4     1 9  1 = 2 9 16. mx  9 n‡j,  4 e 1 m dx Gi gvb KZ? 4ln9 9 4 4 9 9ln4 DËi: 9 4 e ̈vL ̈v:  4 e 1 9 x dx = 9[lnx] = 9(lne 1 4 – ln1) = 9 4 17. [0, 2] e ̈ewa‡Z y = x – 1 Ges y = 0 †iLv Øviv Ave× A‡ji †gvU †ÿÎdj KZ?  2 0 (x – 1) dx  2 0 |x – 1| dx 2  2 1 (1 – x) dx 2  2 0 (x – 1) dx DËi:  2 0 |x – 1| dx e ̈vL ̈v: 2 y = x – 1 1 O – 1 O 1 2 y = |x – 1| X Y Y X X Y  wb‡Y©q †ÿÎdj =  2 0 |x – 1| dx [⸪ †ÿÎdj (+ ve)] 18. d dx        1 0 sin–1 x 1 – x 2 dx Gi gvb KZ? 0 1 2 2  3 DËi: 0 e ̈vL ̈v:  1 0 sin–1 x 1 – x 2 dx =   2 0 z dz =     z 2 2  2 0 =  2 8  d dx      2 8 = 0 awi, sin–1 x = z  1 1 – x 2 dx = dz x = 1 n‡j, z =  2 x = 0 n‡j, z = 0 19.  1 0 1 – x 2 dx = ?  4  2  2 DËi:  4 e ̈vL ̈v:  a 2 – x 2 dx = x a 2 – x 2 2 + a 2 2 sin–1x a + c   1 0 1 – x 2 dx =    x 1 – x  2 2 + 1 2 sin–1 (x) 1 0 = 0 + 1 2   2 – 0 – 0 =  4 20. f(x) =  x 0 x – 9 x 2 + 7 dt n‡j, x Gi †Kvb gv‡bi Rb ̈ f(x) b~ ̈bZg n‡e? 9 3 0 None DËi: 9 e ̈vL ̈v:  a b f(x) dx = f(x)  d dx f(x) = f(x) b~ ̈bZg gv‡bi Rb ̈,  f(x) = 0 x – 9 x 2 + 7 = 0  x = 9