Evaluate the integrals in Exercises 1 to 8 using substitution. 1. 1 2 0 1 x dx x 2. 2 5 0 sin cos d 3. 1 1 2 0 2 sin 1 x dx x 4. 2 0 x x 2 (Put x + 2 = t 2 ) 5. 2 2 0 sin 1 cos x dx x 6. 2 2 0 4 dx x x 7. 1 2 1 2 5 dx x x 8. 2 2 2 1 1 1 2 x e dx x x Choose the correct answer in Exercises 9 and 10. 9. The value of the integral 1 3 3 1 1 4 3 ( ) x x dx x is (A) 6 (B) 0 (C) 3 (D) 4 10. If f(x) = 0 sin x t t dt , then f (x) is (A) cosx + x sin x (B) x sinx (C) x cosx (D) sinx + x cos
Question 1:1 2 0 1 x dx x ✥
Question 2:2 5 0 sin cos d
Question 3:1 – 1 2 0 2 sin 1 x dx x ✩ ✪ ✫ ✬ ✭
Question 4:2 0 x x 2 (Put x + 2 = t 2 )
Question 5:2 2 0 sin 1 cos x dx x ✮ ✯ ✰
Question 6:2 2 0 4 – dx x x ✥
Question 7:1 2 1 2 5 dx x x ✱ ✥
Question 8:2 2 2 1 1 1 – 2 x e dx x x ✩ ✪ ✫ ✬ ✭ Choose the correct answer in Exercises 9 and 10
Question 9:The value of the integral 1 3 3 1 1 4 3 ( ) x x dx x ✲ ✘ is (A) 6 (B) 0 (C) 3 (D) 4
Question 10:If f(x) = 0 sin x t t dt , then f ✳(x) is (A) cosx + x sin x (B) x sinx (C) x cosx (D) sinx + x cos