Question

If ∫ sec²(7 – 4x)dx = a tan (7 – 4x) + C, then value of a is​

Answer 1

Answer:

Ex 7.2, 22 sec 2 7 – 4 Step 1: Let 7 – 4= Differentiating both sides ... 0−4= −4= = −4 Step 2: ... Ex 7.2, 22 - Chapter 7 Class 12 Integrals ... 1 4 tan + = +.

Step-by-step explanation:

Answer 2

Value of a is -1/4 if ∫ sec²(7 – 4x)dx = a tan (7 – 4x) + C

Given:

• ∫ sec²(7 – 4x)dx = a tan (7 – 4x) + C

To Find:

• Value of a

Solution:

• ∫ sec²(x)dx = tanx + C
• ∫ sec²(ax+b)dx = (1/a) tany + C

Step 1:

Assume y = 7- 4x

dy  = -4dx

dx = -dy/4

Step 2:

Substitute 7-4x = y  and dx = -dy/4

∫ sec²(7 – 4x)dx

= ∫ sec²(y)(-dy/4)

= -(1/4)  ∫ sec²(y)dy

Step 3:

Integrate

-(1/4)tany  + C

Step 4:

Substitute y = 7 - 4x

-(1/4)tan(7-4x)  + C

Hence, ∫ sec²(7 – 4x)dx = (-1/4) tan (7 – 4x) + C

Comparing with ∫ sec²(7 – 4x)dx = a tan (7 – 4x) + C

a = -1/4

Value of a is -1/4