Question

Not sure how to appraoch this ? can someone help would really appreciate it

Answer 1

`int_0^2f(x)dx=23`

Explanation:

`int_0^2f(x)dx=int_0^1f(x)dx+int_1^2f(x)dx`

• `int_0^1f(x)dx=int_0^1 5x^9dx=5int_0^1(x^10/10)'dx=`

`5[x^10/10]_0^1=5/10[x^10]_0^1=1/2[x^10]_0^1=1/2(1-0)=1/2`

• `int_1^2f(x)dx=int_1^2 6x^3dx=6int_1^2(x^4/4)'dx=`

`6/4int_1^2(x^4)'dx=3/2[x^4]_1^2=3/2(16-1)=3/2*15=45/2`

Hence, `int_0^2f(x)dx=1/2+45/2=46/2=23`